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Fermat and Van Ceulen Visit 2009 - October 14, 2009
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Spiked Math Comic - Fermat and Van Ceulen Visit 2009

Ludolph van Ceulen spent a large part of his life calculating pi, I think he got up to 35 decimal places.

Spiked Math Comic - Fermat and Van Ceulen Visit 2009

You may have heard of Fermat already. He is best known for Fermat's Last Theorem and the famous "margin" that was too small for his proof. It remained an open problem for over 350 years until the mid 90's.



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16 Comments

Ceulen also taught fencing, opened up a fencing school, and was really good at it. He needs a sword.

I think he taught the Thibault style of fencing, but don't quote me on that.

Thibault style? wat?
Which blade?

The explanations are helpful! I majored in Math and I still sometimes don't get one of the jokes.

And, Fermat was right! The margin was waaaaay too small for the proof. And that's the proof that uses all sorts of esoteric math Fermat would have had to spend a couple of centuries developing.

I don't know which blade Saber.

Ludolf van Ceulen was in the business of making mathematical tables. That was rocket science in those days (navigation, warfare...). The point about getting pi to so many decimal places was to show that he was the best calculator in town. Everyone should come and buy his cosine tables. Amusingly, our notation for decimal fractions had not yet been invented. So he had to write "the ratio of the circumference to the diameter of a circle lies between 3 plus 14159... divided by 100000... and 3 plus 14159 ..... plus 1 divided by 100000....". He had this printed on the dustcover of his books of tables, and also, later, it was engraved on his tombstone in the Pieter's Church in Leiden.

Why not just write 31415926535 8979323846 2643383279/10^31 ?

And founded a fencing school. In those days, picking on geeks could get you killed.

Ah i c the confusion
it says swordsmanship not fencing
i think fencing didn't exist back then
because fencing is a sport whereas swordsmanship is more actual fighting
and has diff sytles and stuff
fencing is just the three diff blades: Foil, Epee and Sabre
and is probably something much more recent wen ppl decided not 2 duel with swords and kill each other
or soemthing

The odd thing is that Wikipedia says fencing
http://en.wikipedia.org/wiki/Ludolf_van_Ceulen

This site says fencing
http://www-history.mcs.st-and.ac.uk/history/Biographies/Van_Ceulen.html

His charter says fencing school.

Dunno.

huh....
well, maybe fencing has evolved then...
a lot

Van Ceulen to calculate PI basically used the half angle formula of Archimedes cotu+cosecu=cot(u/2). A huge amount of iteration is needed to achieve Pi to 20 places of decimals. The cumbersome algebraic iteration is needed in preference to the arithmetic iteration which has rounding off problems.

Further to my comment of 4 December 2011, I have come across another way Van Ceulen could have used to arrive at his value for PI. The half angle formula could be regarded as the first two terms of the following infinite series cotu+cosecu+cosec(u/2)+cosec(u/4) etc=cot(u/n). Cosec or sine tables to a very high number of decimal places would be required. Pi itself would be ncot(u/n).

Further to my comment of 28 December 2011,the sine tables to a very high number of decimal places could with difficulty be computed from the infinite series for sines, sinu=u-u^3/3!etc. Pi itself would be 4ntan(u/n). The expression in my previous comment of 28 December 2011 needs to be inverted to become a tan, apologies.

Further to my comments of Dec 2011, the Archimedes calculation of the cotangents and cosecants of very small degrees involves finding the square roots of numbers containing a high number of digits. Apparently Van Ceulen was able to do this by drawing up tables of squares of consecutive numbers to at least 10 digits. From these tables he is then able to obtain the square roots which he needs for the PI calculation.

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