The Pi Bike is a fully functional bicycle designed by Martijn Koomen and Tadas Maksimovas, handmade from carbon fibre material in the shape of the mathematical symbol, Pi (π).

#### Fermat's Birthday

#### Aug 17

#### Other Scottish Country Dances for this Day

#### Today's Musings, History & Folklore

"It is impossible for any number which is a power greater than the second to be written as a sum of two like powers. I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain." ~ Pierre de Fermat (1607-1665)

"Fermat’s Last Theorem” beguiled mathematicians for over 350 years, until it was proved by Andrew Wiles, with Richard Taylor, in 1995. The famous proposition was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica; Fermat added that he had a proof that was too large to fit in the margin. However, there were first doubts about it since the publication was done by his son without his consent, after Fermat's death. Prior to its proof was in the Guinness Book of World Records as the "most difficult mathematical problem" in part because the theorem has the largest number of unsuccessful proofs.In "The Royale", a 1989 episode of the 24th-century-set TV series Star Trek: The Next Generation, Picard tells Commander Riker about his attempts to solve the theorem, "still unsolved" after 800 years. He concludes, "In our arrogance, we feel we are so advanced. And yet we cannot unravel a simple knot tied by a part-time French mathematician working alone without a computer." Andrew Wiles's insight leading to his breakthrough proof happened four months after the series ended. Mathematicians for the win!

#### Fermat's Bicycle

August 17th marks the birthday of Pierre de Fermat (17 August 1601 (or 1607) – 12 January 1665), a French lawyer and mathematician who is given credit for early developments that led to infinitesimal calculus.

In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of the differential calculus, then unknown, and for his research into number theory. He also made notable contributions to analytic geometry, probability, and optics.

He is best known for his conjecture, usually referred to as "Fermat's Last Theorem," which he famously described in a note (in 1637) at the margin of a copy of Diophantus' Arithmetica. This was first discovered by his son and included the statement that the margin was too small to include the proof.

In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation a^n + b^n = c^n for any integer value of n greater than two.

The first successful proof was released in 1994 by British mathematician Andrew Wiles, using techniques unavailable to Fermat, and formally published in 1995, after 358 years of effort by mathematicians. The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th century. It is among the most notable theorems in the history of mathematics and prior to its proof it was in the Guinness Book of World Records for "most difficult mathematical problems".

See this video below for a good overview of the history of this theorem.

This dance was devised for the Erlangen (Germany) Scottish Country Dance group in August of 1994 in honor of the announcement by Andrew Wiles, in June of 1993, of a proof of Fermat's Last Theorem.

The bicycle motif that occurs in the dance (via wheels and spokes) commemorates the fact that Erlangen is a very bicycle-friendly town. The dance is known as "Das Fermatische Fahrrad" (Fermat's Bicycle) or "August in Erlangen."

For a video of the dance being performed in Fanwood, New Jersey, 2012, see below.

And for more on Fermat, click the artistic rendering of "Fermat's Last Theorem" by artist John Kuhn. It consists of glass pieces arranged as cubes inside this cube which triggered the Fermat's Last Theorem connection on a revolving mirror base. Photo by Al_HikesAZ.