Fifth solution to the Apollonius’ Problem found by Bulgarian student after 2000 years

Radko Kotev, 18, a student in the National Gymnasium of Natural Sciences and Mathematics in Sofia
Photo: ec.europa.eu
The Apollonius' problem formulated in 260 BC was finally solved in Bulgaria only recently. The problem is how to construct circles that are tangent to three given circles in a plane. The notorious puzzle has several variants. Originally the complex geometrical problem was set by Euclid and was further developed by his disciple Apollonius. Its original solution however was lost in the Library of Alexandria fire. So far, only four solutions of the puzzle are known achieved by famous mathematicians. Now Radko Kotev, 18, a student in the National Gymnasium of Natural Sciences and Mathematics in Sofia has become the fifth thinker worldwide to have found a solution to Apollonius’ Problem.

“Now we have powerful computers at hand”, Radko Kotev says. “With just a few clicks of the mouse we are able to wipe out everything in the draft. This helps a lot because we can see things more clearly. I have been using the computer for the things I have tried to solve. I don’t think I would have managed the same results without one.”

Radko Kotev spent two years working on the project. All the way through it, he was assisted by his teacher of mathematics. The young mathematician came up with the solution on an early morning.

“It was so strange”, he says. “I went to sleep that night, thought about the problem, and in the morning I said to myself, why not try this way. I took a sheet of paper, drew up what was needed and the solution came very easily.”

He first showed the solution to his parents who are both mathematicians, and then to his teacher. In this way Radko Kotev has found a solution to a problem that has challenged the humankind for close to 2000 years. At the European contest for young scientists in Lisbon, Portugal, there was keen interest in his project. In competition with 85 projects of students from across the world, Radko Kotev was given the Special Prize of EIROforum, a European NGO uniting 7 European research institutes. The prize included a one-week visit to the Laue-Langevin Institute (ILL) in Grenoble. In early March Radko Kotev will present his project in the world’s most modern research center. From next autumn, he hopes to start studying applied mathematics at the University of Glasgow, Scotland. This is a way for him to make a childhood dream come true – study abroad. Later he plans to be back to Bulgaria.

“I do not imagine that solving the Apollonius’ Problem should open all doors for me. I did it because I found it amusing, not for fame or career prospects. It is also the result of many years of hard work at school. I cannot say that solving this problem has been a great dream of mine – it was fun to do.”

Radko is a modest and easy-going guy. He admits some of his dreams are quite feasible – like visiting the Disneyland in Paris. Unlike his coevals he is not glued to his computer around-the-clock – he just uses it for work. He loves being with friends, reads a lot, and is a John Grisham fan. Radko has grown up in a loving family that has given him all basic values. He wishes to change the world through positive thinking and interesting ideas. What is the secret of his success?

“I have never seen mathematics as a duty. I’ve never though I should solve problems all the time and write endless home works. I have always solved problems for the fun of it. In fact, this is my hobby”, concludes young mathematician Radko Kotev.

Translated by Daniela Konstantinova
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