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Transcript

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2 UPCOMING EVENTS Pascal English Schools Hidden Talents Evening April 16th, 7:30pm University of Cyprus in Nicosia, Main campus auditorium Everyone is invited to come support these students who are competing in a talent show against the other Pascal schools. 15 acts will be showing their talents for 1st, 2nd and 3rd place prizes. Come enjoy the show and cheer for your classmates! Singers Ioanna Georgihiadis 2A Raphael Georgiou 4B Gavriella Tsappi 1A Dancers Kristiana Chrysaphi 3E Elizabeth Karagiorgi 5B Irene Chrystodoulou 5A Kallistheni Karoulla 5B EUROPEAN YOUTH PARLIAMENT 8AM-7PM Sunday March 28th in the English School Students participating: Christiana Charalambous 6B George Pericleous 6A Yiannis A Kounnas 6B Irene Christodoulou 5A Kallistheni Karoulla 5B Teachers Mentors: Mr Elias Kamaratos Mr Micheal Hielscher Mrs Angela Apostolou Mr George Georgiadis Mrs Thekla Papastavrou Activities Team building Conflict resolution Communication skills Problem solving Committee work Discuss issues ideas/issues Brainstorm solutions organize plan to present General assembly Present solutions to group

3 OUR THEATRE PRODUCTION Note from the editor Dear Reader, Usually the P.E.S. year book opens with a prologue, a passage either a poem or philosophical saying followed by an interpretation in the editor s letter, connecting in some-way the theme of the passage to scholastic life. This year we thought we would do something a little different. The observant reader will notice that the page assigned to the poem is simply an empty page commencing with a repetitive series of full stops, alluding to a continuance, a new beginning... It is not for the editors to decipher and convey it s meaning, but rather to stimulate the reader s own ability to ponder what is to follow. For those that are graduating from P.E.S, it is a time to assess their abilities, ambitions and motivations for the future. Some graduates will have to serve their country, others will go off to higher education and others will simply take a break and live a little. For the many that will remain, continuing their secondary education, it is a time to focus on the importance of education. However, it is not, as stated previously, dictum. What is to follow is in the hands of the individual and not defined by a humble passage. The vastness of the unknown, far over- shadows that which is known. Having stated this, whatever path is chosen by an individual, have comfort in the belief that you have gained the knowledge and skills to direct your own life. It is time to write your own passage... Julia Antoniou, IB2 Journey II Random Distance

4 Dear Readers, I look back at the academic year feeling very proud. I am proud of the academic accomplishments of all of our pupils across the various school subjects that we offer under the guidance of our dedicated teachers; International Awards for External Examinations, prizes at various writing competitions the list is endless. I am proud of the very rich program of events offered. Our pupils travelled to Athens to visit the New Acropolis Museum, they visited a vast number of destinations through our clubs and they visited universities in the UK. I am proud of the accomplishments of our athletes that received a large number of medals in track and field and swimming Pancyprian Competitions. Our U15 football team traveled to Dubai and returned with silver medals. I am proud of all the assistance we offered to our local community; we provided needy families with food baskets, assisted a young single mother and her baby to make a brand new start and took part in fundraisers. I am proud of the university offers that our Form 6 pupils received; they leave our school ready to excel in tertiary education. TRIP TO ACROPOLIS MUSEUM Seven years ago when we started our school, we had a vision of what kind of school we wanted to set up. We wanted to create a warm, safe, quiet, happy environment where young people could excel academically and socially. We make that vision reality on a daily basis and as you read through this yearbook, you will get glimpses of all that I am proud of. I look forward to the next academic year with our new school facilities that will make our school an even more exciting place to learn. Despina Lioliou Headmistress Androulla Kakoulli, IB2 (Diptych) TRADITION AND BEYOND 2ND SCHOOL EXCURSION Our Second School Excursion, took place on Wednesday 2nd March. Form 1 and 2 visited Koureion and Kolossi before going to Governor s Beach for Lunch. Forms 3 5 went to Saint Marina Activity Resort where they had the opportunity to try rock-climbing, horse-riding, archery and much more. Form 6 went to the mountains where they prepared their own souvla and got to go on a hike.

5 STUDENT COUNCIL The Staff of Pascal English School Larnaka Student Council Easter Games CLASS PRESIDENTS 1A Paris Zingis 1B Andreas Fokas 1C Antonis Siantanis 1D Andreas Mouzouris 1E Demetris Solomou 2A Mariam Venizelou 2B Stelios Savva 2C Andrea Mavrolefterou 2D Irene Michael 2E Nicholas Psaras 3A Chelsea Smith 3B Rayana El-Baba 3C Fivis Hadjimitsi 3D Evgenios Mavri 3E Yiannis Stylianou 4A Zacharias Kavelis 4B Kyriaki Hadjiconstanti 4C Demetris Valiantis 4D Nicholas Charalambous 5A Pavlos Georgiou 5B Kallistheni Karoulla 5C Marios Karagiorgi 6A George Pericleous 6B Christian Charalambous 6C Ioannis A Kounnas EXECUTIVE STUDENT COUNCIL PRESIDENT Christian Charalambous VICE-PRESIDENT George Pericleous STUDENT RELATIONS OFFICER Ioannis Kounnas A SECRETARY Kallistheni Karoulla TREASURER Irene Christodoulou MEMBER 1 Paris Zingis MEMBER 2 Mariam Venizelou MEMBER 3 Chelsea Smith MEMBER 4 Nicholas Charalambous HONORARY MEMBERS Constantinos Thouppos Stephanie Diakou Nicholas Panayi Our Student Council proved to be very active this year. Its members organized and promoted a large plethora of events for Christmas, Valentine s Day and Easter. Furthermore, they managed to raise 1700 Euros for a single mother and her young 10 month old baby that was starving. Front row from left: Constantia Papamarkou, Christina Thomaidou Pavlides, Soterios Panayi, Marios Hadjivassiliou, Despina Lioliou, Costas Costa, Karen Michael, Elias Kamaratos. Second row: Panny Theodoropoulou, Despina Kaittani, Maria Zingis, Rodoula Anastasiou, Antonis Antonopoulos, Maria Evangelidou, George Klokkaris, George Georgiadis. Third row: Panayiota Athanasiou, Martha Socratous, Stella Charalambous, Margarita Theodoulou, Lena Mahdessian, Eliza Zervou, Anna Shippetaris. Fourth row: Frangesca Frangou, Eleni Christodoulou, Michalis Ellinas, Christina Karaviotou, Maria Ioannou, Irene Petrou, Angela Venizelou, Eleni Ioannou, Simon Phillips. Fifth row: Evey Pistola, Ilianna Tsiapou, Panayiota Demetriou, Georgia Markadji, Thekla Papastavrou, Evanthia Markides, Elpidoforos Anastasiou, Zena Alambriti, Susan Jordan, Maria Theofilou, Maria Anastasiou, Michael Hielscher, Andreas Avraam, Maria Kimmitri. Sixth row: Gregoris Demetriou, Andri Stavrou, Constantina Constantinou, Aspasia Manti, Angela Apostolou, Demos Kaoullas, Christoforos Alexandrou, Petros Kimitris, Socratis Athanasiou. 1A President and Vice-President Promoting Blood Donation Blood Donation 2010 Front row from left: Michalis Kavourides, Andreas Evgeniou, Marios Pavlou, Paris Zingis, Eliana Ioannidou, Tasos Stavrou, Savanna Graham, Rafaella Nicolaidou. Second row: Mr. Antonis Antonopoulos, Elliot Timm, Antonis Georgiou, Charlie Workman, Andreas Lemesios, Nicole Georgiou, Anastasia Kappellou, Fiona Pasiadou, Gabriella Tsiappi, Ms. Aspasia Manti. Third row: Anastasis Kakoullis, Maria Kangeli, Nicoletta Xydia, Natalie Redpath, Demetra Panayiotou, Danae Palate.

6 1B TRIP TO UK VISIT TO UNIVERSITIES Haunted towers, chilling weather and a lot of foreigners, that is what I thought when people talked of England. Not in my craziest dreams I would imagine that I would fall in love with the place! Our trip to England was absolutely fantastic! The weather is not really as cold as you might think. On the contrary I thought it was quite the perfect weather to live in! England is filled with wondrous places to visit! Full of old, symmetrically identical buildings, land territories of green, white and pink! The old towers, still spreading the sense of the old majestic era. It was truly a magic experience. 1C Front row from left: Sophia Charalambous, Georgia Elia, Eleni Georgiou, Nicole Costa, Georgos Pavlou, Constantinos Xydias, Christos Trikomitis. Second row: Mr. Antonis Antonopoulos, Rafaella Solomonidou, Marina Agathocleous, Kyriaki Mavrou, Stalo Vassiliou, Andreas Solomonides, Chrysostomos Constantinou, Charalambos Frangou, Ms. Maria Anastasiou. Third row: Maria Vassiliou, Maria Demetriou, Andria Hadjiyiannakou, Charis Karoullas, Andreas Fokas, Constantinos Iasonides. Fourth row: Barbara Paschali, Demetra Kavallari, Louisa Yiangou, Phillip Travkin. To be honest we did not get much sightseeing because that was not our original aim but still, even that little peek we got enhanced me. The universities were absolutely fantastic. Both students and teachers were extremely friendly and sociable. We have visited various types of Universities both in large cities but also in small towns. We were taken on campus to see lecture rooms, classrooms, libraries with awesome resources and study rooms. One of our major concerns which were accommodation has also been dealt with as we have seen the rooms and halls of residence in all seven Universities we visited. Front row from left: Panayiota Foukkari, Kleopas Kleopa, Rafaella Spanou, Christos Zorpides, Panayiotis Pirillos, Elena Alexandrou, Pantelitsa Stavrou. Second row: Ms. Eleni Christodoulou, Elena Marangou, Anastasis Zinonos, Yiannis Papoulias, Constantinos Zachariou, Costas Sampson, Alexandros Todirica, Panayiotis Christou, Mr. Antonis Antonopoulos. Third row: Chrysanthi Shiantani, Eleni Karamanoli, Kalia Avraam, Iliana Kafatari, Nicoletta Sakka, Nicoletta Vrikki, Georgia Foti, Kyriaki Kadi, Antonis Shiantanis. Sausages for sale on Tsiknopempti Mad Scientists at work!!

7 TRIP TO DUBAI U15 FOOTBALL COMPETITION SPONSORED BY A.THEODOROU DEVELOPERS 1D Team at airport with Sponsor Mr. Estathiou TRIP TO GREECE TO VISIT THE NEW ACROPOLIS MUSEUM There was a draw in the school yard for the trip to Greece, where twenty-five students were drawn from both the lower and upper school of which three were runners-up. The aim of the excursion was to educate and entertain both teachers and students. Woken up early in the morning of departure, we arrived at the New Airport of Larnaca at 6:45. When we saw each other we started whispering and chattering and that was the time the cameras turned on and we started taking photos of silly things while we were spending our time buying gifts and candies for our parents, siblings, relatives, friends and ourselves because we knew that this was a one-day excursion. and we wanted to freeze time by taking photos. Soon it was time to board the plane, we sat in our seats and then when we were allowed to stand up, we all started changing seats, sitting with our friends, playing with the food served, and once again taking pictures. After our arrival in Athens, we got on the bus and we winded our way towards the Acropolis Museum. We finally arrived at our destination. We got off the bus and we followed the instructions given to us. We saw some statues of both men and women and we were given a brief description of how life was in the past. After traveling that long way through the centuries we were starving! Goody s was right there waiting for us after that long, but fun walk through the museum and souvenir shop. Then we got on the bus again and we arrived at the airport where we bought our last gifts and where I forgot my jacket. Unfortunately we had to return back to Cyprus but we really had a great time in Athens, a beautiful city with great architecture and rich culture. Faviola Zimboulaki 5 Our Champions return with Silver Medals!! Our Cheerleaders 1E Front row from left: Mr. Antonis Antonopoulos, Kyriaki Charalambous, Demetris Michael, Efthymia Panayiotou, Eleni Alexandrou, Andreas Sophocleous, Anastasia Andronikou, Georgia Georgiou. Second row: Andreas Mouzouris, Andrea Theodotou, Korina Kyriakou, Demetris Demetriou, Christos Georgiou, Lenos Prodromou, Lazaros Kyriakou, Ms. Maria Ioannou. Third row: Stavrinos Constantinou, Leonidas Solomondos, Georgos Kyriakou, Alexandros Efstathiou, Alexandros Constantinides, Marina Philippou, Nayia Panayi. Front row from left: Loizos Zinonos, Lazaros Markou, Thea Stavrinou, Maria Christou, Electra Pilides, Stephanie Spyrou. Second row: Marios Agathocleous, Marianna Anastasiou, Stylianos Markou, Demetris Solomou, Sophia Koudelis, Savvas Perdios, Angelos Antoniou, Antonis Stavrou. Third row: Mr. Antonis Antonopoulos, Constantina Charitonidou, Miranda Apostolou, Maria Pantziarou, Christina Pilides, Kyriaki Vassiliou, Christiana Nikiforou, Ms. Elina Zervou. Fourth row: Valentina Savva, Demetris Ioannou, Evros Petrides, Andreas Andreou, Nicolas Constantinou.

8 2A Bake Sale Cypriot Dancing 2B Front row from left: Ms. Irene Petrou, Eftychhia Xiourouppa, Charis Xiourouppa, Eleni Alambriti, Andreas Economides, Ioanna Georgiadies, Mariam Venizelou, Andreas Stavrou, Mrs. Angela Venizelou. Second row: Alexandrina Valeva, Michelle Michael, Stavroulla Antoniou Latouros, Curtis Graham, Antonis Zakkeos, Giorgos Takkas, Constantinos Porfyriou. Third row: Kyriaki Hadjiyiasemi, Chrystoforos Thoma, Michalis Xiourouppas, Theodoros Eracleous, Angeliki Ourri, Zacharias Foka. Fourth row: Stavri Hadjigeorgiou, Christiana Mitsidi, Marat Valeev, Rafael Matsangos, Charalambos Lappas, Isabella Panayi, Vasiliki Athanasiou. HOUSE ACTIVITIES Karaoke, Socci, Cypriot Traditions, Band Jamming Grape Stomping Loukoumades for Sale HOUSE CAPTAINS Front row from left: Sophie Galvin, Lauren Leonti, Antonis Yiallouros, Nicholas Kemitzis, Alexandros Pavlimbei, Panayiotis Kontos, Lina Francis. Second row: Ms. Despina Kaittani, Kallia Nathanael, Anna Pashiourtidou, Loukia Liperi, Michalis Mavromatis, Nicholas Panayi, Paraskevi Michael. Third row: Joanna Papamichael, Alexandra Hadjikakou, Emma Ogden, Vasiliki Fouli, Yiannis Spanoudes, Andreas Nicolaou. Fourth row: Savvas Savva, Panayiotis Anastasiou, Stelios Savva, Miltos Solomou, Panayiotis Ppasias, Antonis Siantanis. Apollo Theodoulos Hadjimatheou,Kyriaki Andreou Artemis Hessan Adnani, Eleni Andreou Demetra Iacovos Iacovou, Anna Zachariou Poseidon George Kyprianou, Julia Antoniou HOUSE COMMITTEES Apollo Michael Hielscher, Susan Jordan Artemis Simon Phillips, Aspasia Manti Demetra Christoforos Alexandrou, Tina Constantinou Poseidon Elpidoforos Anastasiou, Despina Kaittani Socci Tournament

9 2C Girls Basketball Team First Aid Lesson Front row from left: Fotoulla Malathoura, Kyriaki Stavrou, Elena Anastasiou, Evdokia Eleftheriou, Irene Nicolaou, Melina Antoniou, Anna Pitta, Theodosis Charalambous, Andronicos Andronicou, Markos Markou. Second row: Ms. Irene Petrou, Marina Kalli, Christina Thouppou, Andrea Mavrolefterou, Vicky Konnari, Stavros Noni, George Mouzouris, Marios Themistocleous, George Papakyriacou, Yiannakis Savvides, Mrs. Maria Zingis. Third row: Michalis Nicolaou, Panayiotis Shiambelas, Petros Anastasi, Efthymia Konatzi, Constantinos Hadjimatheou, Lefteris Sklavos, Theodoros Yiorkas, Andreas Charous, Maria Aresti. 2D Helping those less fortunate at Christmas 1ST SCHOOL EXCURSION Our first school trip took place on Monday, 1st December. Form 1 pupils relaxed at Governor s Beach before visiting the archaeological site at Chirokitia whereas Form 2 pupils went on the longer trip to Agros and specifically to a local sweet -making workshop. Years 3 to 6 had fun bowling at K-Cineplex in Larnaca and shopping at the Mall of Cyprus in Nicosia. Valentine s Day Activities Front row from left: Ms. Irene Petrou, Theodora Kyprianou, Nicoletta Polydorou, Andrea Prastiti, Tonia Yerolemou, Stella Kakoulli, Stephanie Loucaidou, Marios Kyriacou, Andreas Tsikkos, Mrs. Iliana Tsiapou. Second row: Katerina Kyriakou, Natalie Loizou, Maria Moyseos, Maria Charalambous, Irene Michael, Sotiris Alexandrou, Kyriakos Kounnas, Alexandros Nicolaides, Panayiotis Andreou. Third row: Elina Andreou, Anna Nicolaou, Avgousta Papacosta, Moysis Papamoyseos, Christos Nicolaou, Vasilis Christou, Georgos Nicolaides, Yiannis Koumi, Andreas Savva.

10 2E Front row from left: Thanasis Panayi, Kyriaki Theodorou, Georgia Ioannou, Maria Marselli, Kalliopi Athanasiou, Vasilis Vassiliou, Chrystodoulos Solomou, Kyriakos Christofides, Ms. Evanthia Markides. Second row: Elena Patsalou, Gavriella Soteriou, Andria Eleftheriou, Elena Efraim, Chrystalla Maouri, Kyriakos Spyrou. Third row: Maria Georgiou, Constantinos Constantinou, Anastasia Isaak, Fotoulla Malathoura, Nicolas Psaras, Demetris Demou, Demetris Christoforou, Constantinos Mallourides. Effective Home Study Presentation for Form 1 CAREER S FAIR The Careers Evening involved pupils and parents of years 3, 4 and 5, teachers, and of course professionals from a variety of fields. OPTIONS/IB PROGRAMME Curriculum options and the IB Programmed were analyzed and explained on separate days in October for Form 3 and 4 students and parents. Events Photo Gal- 3A Overnight Trip for Form 2 to Ayia Napa Overnight Trip for Form 1 to Agros 28th October Parade Front row from left: Mr. George Klokkaris, Eamonn Jordan, Marina Panayiotou, George Sandler, Pailag Tatarian, George Kazantzis, Andreas Andreou, George Kyriacou, Demetra Georgiou. Second row: Achilleas Eftychiou, Stella Christou, Jennifer Joannou, Vasilia Koumandari, Stephanie Porfyriou, Stella Petrou, Hayley Clark, Ben Timm, Ms. Andri Stavrou. Third row: Stephania Marottou, Andreas Georgiou, Giorgos Iacovou, Varnavas Sisou, Andreas Stylianou, Christodoulos Michael, Dickran Shadarevian, Stelios Petrou, Lida Ketsbaia, Chelsea Smith. 28TH OCTOBER CELEBRATIONS As every year we celebrated the Greek national holiday with choir songs and inspirational speeches. On the 28th selected students successfully represented our school in the parade. Track and Field Day

11 SOLAR CAR CLUB This year the PES Solar Car Club continued the solar car project build that was started last year by Mr. Neophytos Sophocleous and Dr. George Georgiadis. 3B At this time, the car is almost completed and minor body work needs to be done in order the finish. Following this it will be time to get out of school and onto the racetrack for testing. Due to unforeseen illness, Mr. Sophocleous has had to stop teaching at our school in early October. Nevertheless, his guidance and inspiration has allowed Mr. Elias Kamaratos, Dr. George Georgiadis, and Mr. Elpidoforos Anastasiou together with students of Form 6 to continue his vision. Since 1997 Mr. Sophocleous, having had a long passion for photovoltaic technology, has been working with his students on furthering awareness of this renewable energy source in Cyprus as it specifically applies to solar cars. In honour and recognition of Mr. Sophocleous contribution not only to the solar car project but to the Pascal (Larnaca) family in general, our car was renamed in February to NEO 1. In late June 2010 NEO 1 is due to take part in the first ever Cyprus Solar Car Challenge organized by the Cyprus Institute. The Challenge is an endurance race to see which of the participants can make the most rounds of the Daytona Go-Cart racetrack, all using the same fully charged batteries, their solar panels and their ingenuity. Constantia Marangou, IB2 Busy People Earth, People and Sky 3C Front row from left: Mona Noorai, Sophia Tingis, Terpsi Georgiou, Eleni Costa, Rayana El-Baba, Elena Zacharia, Yiannos Aristides, Sergis Nicolaou, Kleitos Mandritis. Second row: Efstathios Efstathiou, Stavros Kasapis, Maria Lingi, Sophie Harris, Christina Kotsapas, Sergios Demetriou, Chrysanthos Stavrou, Ms. Frangesca Frangou. Third row: Despina Xiourouppa, Marianna Theodosi, Danae Zimboulaki, Anna Zonia, Andri Challouma, Melinos Ambizas, Pantelis Xiourouppas, Nicholas Hadjittoouli, Andreas Papachristodoulou, George Alexandrou, Costas Hadjikakou. Whatever the outcome, and we are hopeful of making a good appearance, we have all learnt from this experience in more ways than one. The NEO 1 Team Savvia Iacovou, IB2 The Mechanical Invasion of the Human Thought Front row from left: Andreas Adamou, Anna Loizou, Chrystalla Antoniou, Irene Athanasiou, Ellie Frangou, Christina Kekkou, Haris Tofias. Second row: Maria Sergi, Panayiota Ioannou, Eleni Ioakim, Vasilia Agathocleous, Theodoros Andreou, Fivos Hadjimitsi, Ms. Lena Mahdessian. Third row: Mr. George Klokkaris, Antonia Erotokritou, Minas Zachariou, Panayiotis Alexandrou, Constantinos Pileides. Fourth row: Christodoulos Georgiou, Timotheos Christoforou, Christos Marangos, Paschalis Paschali, Vassilis Kyriacou, Petros Konomou.

12 3D 3E Front row from left: Anastasis Kounnas, Evanthia Stavride, Pantelitsa Hadjiantoni, Maria Philippou, Marisa Avraam, Vasia Parpouna, Ioanna Kyprianou, Irene Theodorou, Ms. Christina Karaviotou. Second row: Ms. Panayiota Athanasiou, Antonis Koudelis, Charalambos Varnava, Constantina Pafiti, Anna Skalioti, Panayiotis Panayiotou, Constantinos Kitsiou, Elias Ioannou, Constantinos Gregoriades. Third row: Michalis Michael, Christos Amirotos, Andreas Marsellis, Demetris Matsoukas, Savvas Parperis, Constantinos Savvides, Evgenios Mavri, Elias Evangelou. HIKING CLUB Footprints in Cyprus Historical Himes The aim of the Hiking Club was twofold: to teach students to enjoy the beauty of nature in Cyprus, while simultaneously visiting sites of geographical, cultural and historical interest. It also aimed to give students a taste of the expedition activity, if they chose to do the Duke of Edinburgh Award. Amongst other places, this year the club visited the traditional craft village of Lefkara, climbed the mountain to the monastery of Stavrovouni, saw the sea caves and coast at Cavo Greko, and trekked from Panagia tou Kambou church to the prehistoric settlement at Choirokoitia. TENNIS CLUB The aim of the club was to introduce pupils to tennis and to teach them to play correctly and understand the game of tennis as well as to teach them some basic techniques and strategies. In the long run, we aspire to create a tennis club that can compete with other schools. PHOTOGRAPHY CLUB The photography club in Pascal English School promoted interest in all aspects of photography as an art form accessible to all, and welcomed student members to enjoy photography at all experience levels. Our members had the opportunity to visit Finikoudes beach in Larnaka and take photos of local people while working, tourists while shopping, people being in cafes and people while walking on the beach. Moreover, students, on their second club day, were asked to bring fashion clothes and get dressed to take pictures in various areas of the school, such as the school yard, parking place and front entrance. Photography is an art in itself that brings about a timeless jewel that is an epitome of perfection. The photography club looks forward to welcome new members in the new academic year and share the passion for photography. SCUBA DIVING CLUB The aim of the Scuba Club was to learn how to adapt to the underwater world and how to set up and use diving equipmen. They were also taught the basic open water skills. Scuba diving means rising (or sinking!) to new challenges. It s one of these rare activities that deliver adrenaline and intensity or serenity and peace. If you seek adventure you will find plenty. If you love nature you will find plenty. If you love nature, you ve come to the right place. If discovery drives you, welcome to inner space. Vikings Diving Center, a great diving school, was approached and all of the lessons were held there. Students had both theoretical and practical lessons. Needless to say the latter was what they enjoyed most!!!! The club had many interesting moments, especially during practical skills. One of the funniest was playing a game underwater, where they had to throw projectiles at each other! Front row from left: Mr. George Klokkaris, Anastasis Michael, Eleni Anastasiou, Constantinos Ploutarchos, Rafael Kanelis, Theodoros Theodorou, Eleni Kyriacou, Louisa Charalambous, Marina Fitiris, Elena Papapanayiotou. Second row: Aristodemos Christoforou, Maria Malathoura, Kyriaki Costi, Andreas Solomou, Kristiana Chrysaphi, Demetris Hadjiconstantinou, Irineos Papouis, Ms. Maria Theofilou. Third row: Maria Perdiou, Irene Adamou, Christina Pascali, Yiannis Stylianou, Demetris Kotsonias. Fourth row: Irene Michael, Alexandra Hadjivassili, Andreas Kyriacou, Neoklis Neokleous, Andreas Hadjiconstanti, Theofilos Christou, Markos Koutsakos.

13 SAILING CLUB The aim of this club was to introduce young children to the exciting sport of sailing in a relatively secure environment. We also focused on fostering team building and building interpersonal skills. THE JAMMING CLUB The Jamming club was the club for students who had any musical talent. The club gave them the opportunity to share their opinions regarding different genres of music. Together they were given the chance to play as a group and 'Jam', showing their musical skills and extend their knowledge. The Jamming club was another opportunity for choir rehearsals for upcoming school celebrations. One important lesson taught in the club was music improvisation. HORSE RIDING CLUB 4A The students had the chance to sail boats on all club days and overall they had a fantastic time as this was a new experience for many of them. THEATRE CLUB The Theatre Club this year gave the chance to our students to get a taste of the background work needed to put together a theatrical production, from make-up artists to workshops on different techniques used by actors and directors. The students had a great experience and took precious memories with them home, memories that will remain with them forever MARTIAL ARTS CLUB Larger than most, the Martial Arts Club went all out this year, attending Sensei Mike s K.O Combats Gym in Aradippou. Equipped with numerous punching bags, weight sets, running machines and an impressive Olympic sized ring, Pascal students had the opportunity to train and get a real taste of how athletes get to professional standards. We sweated our way through various selfdefense techniques, fitness drills and tactics with the guidance of our experienced coach, Mike Prodromou. We d like to hereby thank him for his time, energy and facilities which he gave generously, with no charge at all. Students appreciated how much hard work, discipline and commitment is necessary for martial arts training, specifically in Thai Boxing and Judo. Unique opportunities were given to students to throw Club Leaders Mr Demos and Ms Despina over their shoulders, which did not go wasted! Our club aimed at teaching students how to take care of the horses and finally ride them. All of the club days were spent at Salt Lake Horse Riding Club where the beautiful scenery combined with Thalia's warm and friendly character and made the whole experience memorable! THE MOSAICS CLUB This year, the Mosaics Club enjoyed time creating works of art by decorating mirrors, photo frames and tiles. The outcome was truly commendable. There was a visit to Helen s Mosaic studio in Larnaca where the basic tools and tiles were purchased and we hope that by the end of the year each student will have completed their chosen project. JEWELLERY MAKING CLUB Diamonds are a girl s best friend. Everyone knows that and best of all, the girls in the Jewellery Making Club!!! This year on our club days the girls made wonderful bracelets, beautiful necklaces, trendy earrings, bookmarks and beautiful accessories for their mobiles. They gained not only the knowledge, but the satisfaction as well, to create their own jewellery with their own personal touch and style. The girls creations proved that they enjoyed every minute of our meetings together. There is more to come ladies! 4B Front row from left: Mrs. Panny Theodoropoulou, Alexandros Tingos, Michaella Gennadiou, Christina Nichola, Andria Mosfili, Georgia Christodoulou, Constantinos Hadjichristou, Zacharias Stylianou. Second row: Yiannis Apostolou, Georgia Malathoura, Christina Zachariou, Magdalena Flouri, Chrystalla Havadjia, Maria Demetriou, Irene Kounna, Ms. Maria Evangelidou, Demetris Lappas. Third row: Konstantin Kldiashvili, Yiannis Vassiliou, Petros Kysela, Papi Petrou, Georgos Orphanides, Andreas Demetriou, Marios Manoli, Zacharias Kavelis. Front row from left: George Kyprianou, Christina Sidorok, Rafael Georgiou, Despo Elia, Doinista Psara, Michaella Savva, Chrystalla Kounna. Second row: Ms. Evey Pistola, Lefteris Kleanthous, Katerina Christofi, Theodora Andronicou, Kyriaki Hadjicosti, Behine Behnejad, Alexandra Shanina, Patricia David, Sophia Lambrou. Third row: Ioannis Toumazou, Kirill Kldiashvili, Soteris Savva, Rafael Georgiou, Michalis Kyriakou, Michalis Challoumas, Antonis Michael, Kyriakos Patsalos, Stavros Timotheou, Ms. Maria Evangelidou.

14 4C 4D Front row from left: Epiphanios Kounnas, Savina Assioti, Natalie Pouli, Rafaella Vassiliou, Christiana Michael, Maria Charalambous, Danae Ellina. Second row: Demetra Kostrikki, Savvas Alambritis, George Zourides, Chrystalla Pavlou, Marios Menelaou, Michalis Pasialountas, Ms. Martha Socratous. Third row: Ms. Maria Evangelidou, Anna Pavlou, Christiana Eftychiou, Demetris Valiantis, Alkaios Petrides, Andreas Zachariou. Fourth row: George Koumandaris, Georgos Panayiotou, Toumazos Charalambous, Constantinos Demetriou, Socratis Manentzou. Front row from left: Varvara Stavrou, Elena Papageorgiou, Nicoletta Eracleous, Georgia Sakka, Andri Constantinou, Loukia Ioannou, Theodora Makri. Second row: Ms. Maria Evangelidou, Rafaella Kekkou, Stella Issa, Andreas Louca, Georgos Georgiou, Kyriacos Papacostas, Ms. Panayiota Athanasiou. Third row: Yiannos Hadjimatheou, Emmanuel Papoulias, Constantinos Pelides. Fourth row: Alexandros Challoumas, Marios Pavlou, Panos Zaouras, Stelios Vassiliou, Nicholas Charalambous, Christoforos Zinonos. CHARITY CLUB The aim of our club was to make students more sensitive about issues concerning our fellow human beings. To encourage students to offer love and support and to accept other people who are in different difficult situations. We organised visits to various foundations and fund raising events. Our activities were as follow: Trip to the foundation of Steliou Ioannou Making Christmas decoration Visit to the hospital in Larnaka and the old age home Agios Georgios Making Easter Candles and sell them for Charity purposes. There was an overall benefit to all club members! CYPRUS HERITAGE CLUB Cyprus Heritage Club was the newly born club of our school. The aim of the club was to give the pupils a little taste of our culture by looking at cultural and traditional aspects of Cyprus. Our first visit was at Lefkara village where the students had the chance to visit the handicraft museum. The next visit was at Nicosia and Laiki Geitonia. Finally we visited Mazotos and the new sculptural museum. The club had many interesting moments especially during the tours. Overall, we had a great time! ENVIRONMENTAL CLUB Our club was small but we were all interested in our environment! On our club days we cleaned beaches by removing litter, visited Rizoelia National Park in order to see nature in all its natural glory, and learnt about the feeding habits of the flamingos at Larnaca Salt Lake. A special thanks to Mr Costas from Larnaca Municipality who talked to us both about the serious litter problem in Cyprus but also explained all about the flora and fauna found locally. DANCE CLUB The aim of the club was to develop the dancing skills of the students in different types of dances such as Street Dance, Salsa, Latin, and Greek dances. Students visited Mambo Dancing School every club day. There, students had the chance to learn the basic steps of the different dances. On our last club day students voted which dance they would like to learn better. CYPRUS HERITAGE CLUB Cyprus Heritage Club was the newly born club of our school. The aim of the club was to give the pupils a little taste of our culture by looking at cultural and traditional aspects of Cyprus. Our first visit was at Lefkara village where the students had the chance to visit the handicraft museum. The next visit was at Nicosia and Laiki Geitonia. Finally we had visited Mazotos and the new sculptural museum. The club had many interesting moments especially during the tours. Overall, we had a great time! WATER SAFETY CLUB This year the water safety club comprised 14 students from years 4 and 5 and two co-ordinators; Petros Kimitris and Aspasia Manti. The aim of our club was to learn water safety skills in case of an emergency. We used two lanes at the outdoor heated pool at the Larnaca Municipal Athletic Centre GZZ for our training. The skills learnt included entering water safely, swimming underwater and rescuing someone in the pool. Our training was followed by a brisk walk to the K-cineplex centre for lunch after an exhausting but enjoyable day at the pool.

15 CIVICS Larnaca Police station. Students were given a talk about juvenile delinquency and they were also given information about road safety. They were also given a tour to different police departments. City Hall At the City Hall the students were given a talk about how the city works / different responsibilities of each department/ Plans about changing Pale Pasha seafront. Students raised some issues about recycling facilities in Larnaca GARDENING This year Gardening Club planted with much success red soil potatoes, celery, green onions, coriander, parsley, rocket, and carrots. In addition, to planting and preparing the soil for planting and growing various vegetables that were picked and eaten during the Easter fast!. We also visited the Athalassa Park where we were familiarized with flora and fauna native to Cyprus and were given a tour of the nature reserve. COOKING CLUB Our students had the opportunity to have hands on experience in cooking. They were able to prepare delicious food and deserts with the guidance of their teachers and a qualified chef from Nicosia. Our activities were based at school and students were able to watch fun programs related to cooking and to demonstrate their knowledge! FAITH CLUB Our club aimed to introduce students to the main faiths of the people of Larnaca by visiting places of worship in the district. After a presentation of the buildings to be visited this year and their significance, the club members boarded the bus for Faneromeni to see the old and new Faneromeni churches and catacomb, the Metropolis area to see Terra Santa church, the Tusla mosque and the Church of our Saviour, Kiti to see Angeloktisti church and the Salt Lake area to see Hala Sultan Tekke and have a picnic. On other club days we visited St. Lazarus church, the Kebir and Z a c h o u r i mosques, St. Helena s Anglican church and the International Evangelical church before heading for Xylotymbou to see St. Marina and Raphael convent and Troulli where we visited St. George monastery. FILM CLUB The main aim of the club is to inform students about filming and help them explore, and at the same time entertain them. Information regarded the broader concept of film industry, and in particular students learned how and where they are produced and they met some people who usually take part in filming. Students had the opportunity to explore some of these aspects themselves by carrying out their own research on specific topics and by visiting places that had to do with film production, TV broadcasting, as well as presentations of movies either in class or at cinemas. 5A 5B Front row from left: Eleni Demetriou, Nicole Koutsofta, Nicoletta Petrou, Krystie Joannou, Irene Christodoulou, Maria Kyriacou, Andri Xiourouppa, Mr. George Georgiadis. Second row: Ms. Thekla Papastavrou, Andreas Theodorou, Theocharis Panayi, Anastasis Apostolou, Yiannis Chasapis. Third row: Leonidas Georgallides, Maria Pavlidou, Christopher Georgiou, Pavlos Georgiou, Andreas Andreou, Michalis Challoumas. Fourth row: Georgia Hadjiconstantinou, Marcel Valeev, Spencer Critchley, Joshua Schoffield, Pike Connor, Jack Petrou. Front row from left: Mr. Elpidoforos Anastasiou, Anastasia Matsangou, Panayiotis Artemiou, Irene Chrysantou, Despo Erotokritou, Andrea Santi, Gabriella Kazamia, Mr. George Georgiadis. Second row: Irene Loucatzie, Elizabeth Karagiorgi, Kallistheni Karoulla, Kallistheni Symeou, Demetra Shadarevian, Marios Michael, Theophanis Phokou, Sergios Sergiou, Douglas Carr. Third row: Illane Papamichael, Kleopas Palate, Valentinos Damianou, Demetris Demetriou A, Georgos Hadjisavva, Zanettos Fitiris, George Kyriacou, Constantinos Patsalos, Gregoris Pittarides, Alexander Critchley, Constantinos Pouyioukka, Christos Demetriou.

16 5C 6A Front row from left: Ms. Panayiota Demetriou, Andri Christofidou, Iacovina Iacovou, Myria Toumazou, Sophia Pericleous, Anthea Koursari, Mr. George Georgiadis. Second row: Michalis Alambritis, Charalambos Athanasiou, Marios Karagiorgi, Marilena Iacovou, Faviola Zimbouliaki, Thekli Louca, Marinos Marinou. Third row: Andreas Ioulianou, Christiana Erotokritou, Demetris Demetriou E, Neophytou Andreas. Fourth row: Andreas Sophocleous, Anastasis Iacovou, Michalis Andronicou, Demetris Georgiou, Andreas Patsalos, Christodoulos Monoyios. Front row from left: Savvia Iacovou, Constantina Marangou, Marina Pasialounta, Natalia DeBenedicts, Haris Constantinou. Second row: Mr. Marios Hadjivassiliou, Ms. Maria Kimmitris. Third row: Constantinos Thouppos, Elena Pitta, Helen Artemi, Stephanie Diakou, Skevi Karaiskaki, Kyriaki Hadjipapa, Alexandros Pizkitzis. ARCHERY Our 25 young Robin Hoods were eager during our first club Day in October to start shooting their arrows. It was a slow start, first having to hand out their new equipment then to learn the rules of safety together with the technical basics of Archery, but once they got going, there was no stopping them. Mr. Elias Kamaratos, Mr. Sotirios Panayi and later in the year Mr. Gregoris Demetriou all worked very hard to make our time shooting arrows enjoyable, safe and productive.archery club members are asked to attend Thursday afternoon Archery Club practice in order to further improve their skills. It paid off because at our regional (Larnaca-Lefkosia) tournament in February we came home with 3 cups (Under 12 Category) ART For this academic school year, the art club focused on a variety of fun and creative activities. With just a few splashes of paint, the magic of colour transformed, some classroom areas into warmer and stimulating learning environments. This year s wall mural theme was inspired by animal prints of identity. The second club day set a festive mood for creating a wonderful selection of Christmas ornaments that were sold to raise fund donations towards charity. The Easter crafts were an all time favorite to take home. Of course, having taken into consideration all the academic hard work, an art therapy session with the drama therapist Roulla Demetriou lit up face in the art room. All art club students were encouraged to approach the concept of art through a different creative means of self expression. FIRST AID First aid - the care given before emergency medical help arrives - can mean the difference between life and death. In First Aid Club, students learnt basic first aid skills such as CPR, guided by an instructor (MEDIC First Aid training programs). This was a very useful club and students participating were issued with an internationally acknowledged certificate. ANIMAL WELFARE The Animal Welfare Club was set up to raise awareness of the necessity to protect animals and care for them properly both physically and psychologically. Throughout this year the Club visited the BFAWS Trust at Dhekelia, where the participants were given a tour of the premises and a presentation on the history and work of the Trust. The children had the chance to play with the animals and were encouraged to participate on a voluntary basis in helping to walk the dogs and/or visit them. The aim of the club is for the participants in the Club to have learned a little about how to care for the animals in our environment and have learnt a sense of responsibility towards our many fourlegged friends! BOWLING Clubs We had the chance to visit the two bowling centres of Larnaca, K-Max and Rock N Bowl. The students were able to learn the different bowling techniques and develop their skills to strike. They were also able to compete with each other and with the other teams and at the same time to build team spirit. At all club days they had lots of fun!

17 Σημαντικότητα των μαθηματικών στη ζωή μας 6B Kατά τη διάρκεια της ανθρώπινης ιστορίας, υπήρξαν και ακόμα υπάρχουν πολλοί εξαίρετοι μαθηματικοί, όχι μόνο που δίδαξαν τις μαθηματικές θεωρίες σε εμάς, αλλά και που βρήκαν ή τουλάχιστον προσπάθησαν να βρουν λύσεις σε διάφορα μαθηματικά ερωτήματα που απασχολούσαν τους ανθρώπους όλων των εποχών. Όλοι αυτοί λοιπόν, φρόντισαν να μας μάθουν ή αλλιώς να διαδώσουν την αξία των μαθηματικών στην ζωή μας. Αν και αρκετοί άνθρωποι δεν την γνωρίζουν και θεωρούν πως τα μαθηματικά είναι διάφοροι τύποι και μπερδεμένοι αριθμοί που κάνουν περίπλοκη την ζωή μας, πιστεύουμε πως πρέπει όλοι μας να μάθουμε την αξία των μαθηματικών. Τα μαθηματικά είναι και αυτά μια επιστήμη και είναι απαραίτητα και πολύ σημαντικά στην ζωή μας. Είναι χρήσιμα σε κάθε τομέα εργασίας, αλλά επίσης μας βοηθούν να κατανοήσουμε διάφορα γεγονότα της καθημερινής μας ζωής. Πολλά πράγματα πρώτης ανάγκης πάλι είναι βασισμένα στα μαθηματικά, όπως τα ρούχα που για να ράψεις πρέπει να μετρήσεις διαστάσεις. Τα Μαθηματικά έχουν τεράστια εφαρμογή στην μηχανική, αστρονομία, πληροφορική, μετεωρολογία, οικονομικές επιστήμες και σχεδόν σε κάθε πτυχή της ανθρώπινης δραστηριότητας. Τα μαθηματικά είχαν αναπτυχθεί για να αποτελούν το προϊών της ανθρώπινης σκέψης και χρησιμοποιήθηκαν στη δομημένη λογική και φιλοσοφία. Άρα όλοι οι άνθρωποι και ειδικά εμείς οι μαθητές, πρέπει να λάβουμε πιο σοβαρά υπόψη μας τα μαθηματικά. Η εργασία αυτή μας έδωσε την ευκαιρία να δούμε τα μαθηματικά από μια διαφορετική οπτική γωνιά. Για παράδειγμα η εικασία του Goldbach, μια εικασία που ταλαιπωρεί εδώ και χρόνια τους μαθηματικούς, έγινε πολύ εύκολα κατανοητή από εμάς. Έτσι και εμείς αισθανόμαστε τυχεροί που βρέξαμε έστω και λίγο τα πόδια μας στην βαθιά θάλασσα των μαθηματικών! Front row from left: Stevie Georgiou, Julia Antoniou, Eleni Andreou, Daniella Kypri, Irene Poupazi, Iacovos Iacovou. Second row: Mr. Marios Hadjivassiliou, Mr. Petros Kimmitris. Third row: Aris Constantinou, Ermioni Yiassoumi, Frosoula Pafitis, Maria Moskofian, Natasa Andreou, Irene Nicolaou, Stelios Lazarou. Fourth row: George Kyprianou, Nicholas Panayi, Stelios Constantinou, Michalis Hadjiantonis. 6C Lito Ellina, 6B Coffee Cup Fairytales George Kyprianou, IB2 The Residue of Today. Front row from left: Evgenia Theodotou, Tarso Theophanous, Mikaella Anthimou, Chrystalla Kailas, Anna Anna Zachariou, Androulla Kakoulli, Kyriaki Andreou. Second row: Mr. Marios Hadjivassiliou, Christina Theodorou, Ioannis Kounnas E, Lito Ellina, Ionanis Kounnas S. Leonidas Charalambous, Panayiota Epifaneiou, Mrs. Rodoula Anastasiou. Third row: Demetris Kounnas, George Exadaktylos, Marios Symeou, Theodoulos Hadjimatheou, Ioannis Kounnas A.

18 TIME What is time really? It s nothing to me What is time really? It s all that we see What is time really? A tick and a tock What is time really? Just numbers written on a clock What is time really? A sunrise, a sunset What is time really? A lucky guess, a bet What is time really? The day or the night Maybe time is really Just dark and light Diamante Poems Love Honest Lovable Kissing Hugging Believing Heart Gift Knife Gun Killing Loathing Shooting Dishonest Horrible Hatred LIFE WONDERFUL AMAZING LAUGHING BAPTIZING ENJOYING OXYGEN WATER GRAVE WEAPON CRYING BURYING PRAYING UNBEARABLE UNFORTUNATE DEATH Jennifer Joannou, 3A Gabriella Soteriou, 2E Lambros Theodorou, 2E αυτήν την θεωρία και έτσι, παραμένει ακόμα μέχρι και σήμερα ανοιχτή. Συνεχίζει βέβαια να απασχολεί διάφορους μαθηματικούς και αποτελεί θέμα συζήτησης ανάμεσα σε μαθητές όπως εμάς που την επιλέξαμε ως θέμα της εργασίας μας. Λόγοι επιλογής αυτού του προβλήματος ανάμεσα σε τόσα άλλα προβλήματα που απασχόλησαν τους μαθηματικούς Πρέπει να σας αναφέρουμε πως μας έχει κινήσει ιδιαίτερα την περιέργεια και το ενδιαφέρον η εικασία αυτή και γι αυτό θέλαμε να την διερευνήσουμε καλύτερα και να μάθουμε περισσότερα πράγματα και πληροφορίες γι αυτήν. Το πιο προκλητικό σε αυτή την εικασία είναι ότι αποτελεί μια τρομακτικά απλή πρόταση, μια πρόταση που και ο μέσος μαθητής Λυκείου δεν έχει καμιά δυσκολία να κατανοήσει. Μια πρόταση που όλος ο κόσμος θεωρεί αληθινή αλλά που κανένας δεν μπορεί να αποδείξει την αλήθεια της! Παραξενευτήκαμε ιδιαίτερα με το γεγονός ότι μία τόσο εύκολη και απλή θεωρία, που μπορεί να την κατανοήσει οποιοσδήποτε, ακόμα και ένας που δεν κατέχει και ιδιαίτερες γνώσεις στον τομέα των μαθηματικών, δεν κατάφερε να καταλήξει σε μία άκρη, σε ένα συμπέρασμα και έχει μείνει άλυτη. Αυτός λοιπόν είναι ο κυριότερος λόγος για τον οποίο διαλέξαμε αυτό το θέμα και μέσα από τη μελέτη μας, πιστεύουμε πως πολύ δύσκολα θα αποδειχθεί αυτό, αφού δεν υπάρχει τέλος στους αριθμούς. Έτσι, δεν μπορούν να δοκιμαστούν όλοι οι θετικοί άρτιοι αριθμοί για να δούμε αν πράγματι ισχύει αυτό! Παρόλα αυτά, δεν πρέπει να είμαστε απαισιόδοξοι! Ίσως με το πέρασμα του χρόνου, να βρεθεί μία άλλη, διαφορετική λύση, η οποία να μην συμπεριλαμβάνει την δοκιμή με όλους τους άρτιους θετικούς ακέραιους αριθμούς. Μαθηματικά μυθιστορήματα και πως αυτά έκαναν την επιστήμη των Μαθηματικών λιγότερο απρόσιτη στους μη μαθηματικούς Η Εικασία του Goldbach έγινε γνωστή στο ευρύ κοινό κυρίως μέσα από το βιβλίο του Απόστολου Δοξιάδη «Ο Θείος Πέτρος και η εικασία του Goldbach». Το βιβλίο αυτό είναι ένα από τα πρώτα μαθηματικά μυθιστόρημα και έχει να κάνει με ένα παιδί το οποίο θέλει να γίνει μαθηματικός ακολουθώντας τα βήματα του θείου του, ενός μαθηματικού που πέρασε όλη του τη ζωή προσπαθώντας να αποδείξει την Εικασία του Goldbach. Τα τελευταία χρόνια, έχουν γραφτεί αρκετά λογοτεχνικά βιβλία τα οποία βασίζονται στα μαθηματικά, γνωστά και ως μαθηματικά μυθιστορήματα. Βιβλία όπως «Το Θεώρημα του Παπαγάλου», «Πυθαγόρεια Εγκλήματα», «Το τελευταίο παραμύθι του Μιγκέλ Τόρρες ντα Σίλβα», «Καταραμένα Μαθηματικά», αλλά και πολλά άλλα, παρουσιάζουν σημαντικά θεωρήματα των μαθηματικών με ένα πολύ απλό τρόπο. Μέσα από τα μαθηματικά μυθιστορήματα, των οποίων οι συγγραφείς είναι πολλές φορές μαθηματικοί, γίνεται προσπάθεια να φτάσουν τα μαθηματικά σε όλο τον κόσμο. Επίσης, μέσα από αυτά γίνεται προσπάθεια, να αγαπήσουν οι αναγνώστες τα μαθηματικά και να κατανοήσουν ότι δεν είναι σε καμιά περίπτωση, ένα μάθημα βαρετό και δυσνόητο. Αξίζει να αναφέρουμε ότι μετά από την τεράστια απήχηση που είχαν κάποια από αυτά τα μυθιστορήματα στον κόσμο, τα μαθηματικά άρχισαν να αντιμετωπίζονται με ένα διαφορετικό μάτι. Η πεποίθηση ότι κάποιος θα έπρεπε να είναι διάνοια για να ασχοληθεί με τα μαθηματικά σταδιακά καταρρίφθηκε. Κάτι τέτοιο μπορεί να βοηθήσει τους ανθρώπους να κατανοήσουν το πόσο σημαντικά και χρήσιμα είναι τα μαθηματικά στη ζωή μας. Maths

19 Οι εικασίες για τις οποίες αλληλογραφούσαν ο Goldbach και ο Euler, έχουν συγκεκριμένα ονόματα, ώστε να μην τις μπερδεύουμε. Η προγενέστερη, δηλαδή αυτή του Goldbach, είναι σήμερα γνωστή ως τριαδική, ενώ η μεταγενέστερη, αυτή με την οποία απάντησε ο Euler, χαρακτηρίζεται ως ισχυρή ή δυαδική. Μετά λοιπόν και από παρέμβαση του Euler, η Εικασία πήρε τη μορφή που έχει σήμερα. Ο Euler, αφού συμπλήρωσε τη θεωρία, τη δέχτηκε ως ένα πλήρως ορισμένο θεώρημα παρόλο που δεν κατάφερε να αποδειχθεί πλήρως, αλλά αποδείχθηκε μόνο ως ένα σημείο. Είναι γι αυτό ακριβώς τον λόγο που ονομάζεται μέχρι και σήμερα Εικασία. Ένας εξαιρετικός ορισμός της λέξης «εικασία» δίνεται στο μυθιστόρημα του Ντένι Γκετζ «Το θεώρημα του παπαγάλου». «Φαντάσου μια ήπειρο, για την οποία η ανθρωπότητα θα είχε τη βεβαιότητα της ύπαρξής της αλλά δεν θα έβρισκε κανέναν τρόπο πρόσβασης. Αυτό είναι μια μαθηματική εικασία!». Οι αποδείξεις όλων αυτών των θεωριών, αφού όπως κάθε σημαντικό ή ασήμαντο γεγονός χρειάζεται μια πειστική δικαιολογία για να εξηγηθεί, έτσι και στα μαθηματικά η απόδειξη είναι η διαδικασία με την οποία η βεβαιότητα για την αλήθεια των αρχικών υποθέσεων ενός προβλήματος μεταφέρεται αναλλοίωτη στα συμπεράσματα. Όπως είπε και ο Hilbert, μετά από τη συζήτηση για το θεώρημα της «Μη Πληρότητας», συχνά τίθεται η απορία αν πρέπει ή όχι να προσπαθούμε για την απόδειξη μιας εικασίας. Σύμφωνα με το θεώρημα της «Μη Πληρότητας» κάθε υπόθεση ή εικασία που παραμένει αναπόδειχτη μπορεί να είναι και εκ των προτέρων μη αποδείξιμη. Σύμφωνα λοιπόν με την Εικασία του Goldbach, όπως καθιερώθηκε να ονομάζεται, κάθε άρτιος (ζυγός) αριθμός μεγαλύτερος του 4, μπορεί να εκφρασθεί ως το άθροισμα δυο πρώτων αριθμών. Με αυτό, εννοούμε πως έστω ένα ζευγάρι αριθμών που είναι άθροισμα του θετικού άρτιου να είναι πρώτοι. Για παράδειγμα, το 6 = = = ή = = ή Ο Schnirelman, το 1939, απέδειξε ότι κάθε ζυγός αριθμός μπορεί να γραφτεί ως το άθροισμα όχι περισσότερων από πρώτους αριθμούς, κάτι που φαίνεται μάλλον απομακρυσμένο από την απόδειξη για δύο πρώτους. Ο Pogorzelski, το 1977, ισχυρίστηκε ότι απέδειξε την Εικασία του Goldbach, αλλά η απόδειξη του δεν έγινε αποδεκτή. Ο Ρώσος μαθηματικός Vinogradov, πλησίασε περισσότερο από όλους, μιας και μέσα από τα θεωρήματα που απέδειξε, βγαίνει το συμπέρασμα ότι η Εικασία του Goldbach ισχύει για σχεδόν όλους τους ζυγούς αριθμούς. Είναι σημαντικό να τονίσουμε πως την Εικασία του Goldbach, έχουν ενισχύσει ισχυρότατοι ηλεκτρονικοί υπολογιστές, που έχουν αποφανθεί ότι πράγματι αληθεύει ως τον 17 αριθμό Κατά διαστήματα γίνονταν πιο εντατικές προσπάθειες για την απόδειξη της. Από 10 Μαρτίου του 2000 μέχρι τις 20 Μαρτίου του 2002, έγινε μια μεγάλη προσπάθεια για την εξεύρεση της κατάλληλης αλυσίδας λογικών συλλογισμών που αποδεικνύουν την αλήθεια, όταν ο εκδοτικός οίκος Faber and Faber πρόσφερε το βραβείο του ενός εκατομμυρίου δολαρίων σε όποιον αποδείκνυε την εικασία του Goldbach, μέσα στο πιο πάνω χρονικό διάστημα. Δυστυχώς όμως, ούτε με αυτόν τον τρόπο κατάφερε κάποιος να αποδείξει Students of Year 5 making a presentation as part of their English lesson English Kyriaki Hadjipapa, 6A Concealed, Revealed

20 Service above Self Undoubtedly service above self is what all of us have grown up knowing to be honorable. I always wonder what it is that motivates someone donate a few coins, and others give up their time and family for voluntary charity work. Out of habit I always contribute towards Oxfam and Unicef, donating an odd five euro doesn't have a profound effect on my life. I didn t acknowledge how and where it would be spent until I was sitting with a group of friends when an old beggar in rags approached our table and asked for money. As I had previously given money to her I hesitated to reach for my purse thinking she was a fraud, but made an offering anyway in the hope that she would leave. After blessing us all, she tottered away leaving us perplexed. We inevitably discussed her condition and other innumerable people like her. When we donated money to charities we wondered, Did our donations actually reach the needy?. Did we need to receive help in order to give it?. All these questions troubled me and I yearned to resolve them. It is an unquestionable fact that without the charity organizations and various humanitarian aid millions of people s suffering would extend to death. Influential people such as Princess Diana, Oprah Winfrey and others like them are inspirational leaders who have helped thousands of children with their donations. Previous to my conscious awareness of poverty, I was selfish in taking my fortunate situation. I was unaware of just how much those loose coins I had and donated could help others. We are fortunate yet we are often too consumed by our own problems that are insignificant compared to more severe problems facing others. We can all experience the exhilaration that altruism brings if we only venture forth in our mind s eye and place ourselves in the shoes of those we wish to help - then maybe we could empathise and realise that we are all connected as humans and that if we don t help each other, then we can never hope to feel the true beauty of giving or receiving that simply defines our existence. Stephanie Diakou, 6B Τα προβλήματα αυτά έγιναν γνωστά πολύ γρήγορα και πολλοί ήταν οι επιστήμονες που έσπευσαν να ασχοληθούν με αυτά. Αρκετά από τα προβλήματα που δόθηκαν τότε επιλύθηκαν εντελώς ή εν μέρει ενώ κάποια άλλα παραμένουν άλυτα μέχρι και σήμερα. Κάποια από τα προβλήματα τα οποία παραμένουν άλυτα μέχρι και σήμερα είναι: Το πρόβλημα των τέλειων αριθμών. Όπως είναι γνωστό, τέλειος είναι ο αριθμός πού ισούται με το άθροισμα των γνήσιων διαιρετών του. Για παράδειγμα, το 6 αποτελεί τέλειο αριθμό διότι ισούται με το άθροισμα των τριών γνησίων διαιρετών του 1, 2, 3. Μέχρι σήμερα γνωρίζουμε ότι όλοι οι τέλειοι αριθμοί είναι άρτιοι. Δεν έχει αποδειχθεί ότι υπάρχουν μονοί τέλειοι αριθμοί ή άπειροι τέλειοι αριθμοί. Το πρόβλημα των φίλιων αριθμών. Οι φίλιοι αριθμοί είναι εκείνοι που ο καθένας τους ισούται με το άθροισμα των γνήσιων διαιρετών του άλλου. Για παράδειγμα φίλιοι είναι το ζεύγος των 284 και 220 διότι οι γνήσιοι διαιρέτες του 284 είναι οι 1, 2, 4, 71, 142 και δίνουν άθροισμα 220, ενώ οι διαιρέτες του 220 είναι οι 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110 που δίνουν άθροισμα 284. Είναι άγνωστο αν αυτοί οι αριθμοί είναι άπειροι. Πρώτοι αριθμοί. Είναι οι αριθμοί που διαιρούνται ακριβώς με το 1 και με τον εαυτό τους (2, 3, 5, 7, 11...). Γενικά οι πρώτοι αριθμοί είναι αυτοί που «βασάνιζαν» και συνεχίζουν να «βασανίζουν» τα σπουδαία κεφάλια των μαθηματικών. Μερικά από τα ερωτήματα είναι: υπάρχουν άπειρα ζευγάρια πρώτων αριθμών που να διαφέρουν κατά δύο μονάδες δηλαδή ζευγάρια δίδυμων πρώτων; Υπάρχει πάντα ένας πρώτος αριθμός ανάμεσα στα τετράγωνα δύο διαδοχικών ακεραίων; Υπάρχουν άπειροι πρώτοι ρ ώστε να είναι πρώτος και ο 2ρ+1; Αρκετά είναι τα βιβλία τα οποία γράφτηκαν με αφορμή κάποια από αυτά τα προβλήματα και πολλοί είναι οι Μαθηματικοί που αφιέρωσαν ολόκληρη τη ζωή τους στην επίλυση αυτών των προβλημάτων. Αυτό οφείλεται, εκτός άλλων και στο γεγονός ότι πολλά από τα προβλήματα που έθεσε τότε ο Hilbert ήταν πολύ εύκολα στην κατανόησή και τη διατύπωσή τους, όπως την Εικασία του μαθηματικού Christian Goldbach. Για τα προβλήματα που μένουν άλυτα ακόμα και σήμερα το Clay Mathematics Institute της Μασαχουσέτης προσφέρει ένα μεγάλο χρηματικό έπαθλο. Όποιος καταφέρει να λύσει ένα από τα 7 προβλήματα της νέας χιλιετίας όπως ονομάζονται, συμπεριλαμβανομένου και των προβλημάτων του Hilbert, θα πάρει το μαγευτικό έπαθλο του ενός εκατομμυρίου δολαρίων. Ιστορικά στοιχεία για την Εικασία του Goldbach Ο Christian Goldbach, ένας σπουδαίος Πρώσος μαθηματικός, σε μια επιστολή του στις 7 Ιουνίου του 1743 προς τον επίσης σπουδαίο επιστήμονα Leonard Euler, αναφέρθηκε πρώτος στην Εικασία αυτή. Ισχυρίστηκε ότι κάθε άρτιος (ζυγός) αριθμός μεγαλύτερος του 2, μπορεί να εκφραστεί ως το άθροισμα δυο πρώτων αριθμών. Είναι σημαντικό βέβαια να τονιστεί ότι εκείνη την εποχή, το 1 θεωρείτο πρώτος αριθμός, κάτι που καταρρίφθηκε κάποιες δεκαετίες αργότερα. Ο Euler, του οποίου τα ενδιαφέροντα απλώνονταν σε ένα πολύ ευρύ φάσμα, διαισθάνθηκε αμέσως ότι η πρόταση αυτή έπρεπε να ισχύει αλλά δεν ασχολήθηκε σοβαρά με την απόδειξή της. Απλά, απάντησε στον Goldbach με μια ισοδύναμη εκδοχή της εικασίας, δηλαδή πως κάθε άρτιος ακέραιος μεγαλύτερος του 2 μπορεί να γραφτεί ως άθροισμα δυο πρώτων αριθμών, ενώ ο Goldbach του είχε στείλει μόνο πως κάθε ακέραιος αριθμός μπορεί να είναι άθροισμα δύο πρώτων. Maths