Wednesday, August 17, 2011

Fermat, well, no, Pythagoras

If Google is your home page (it's mine), you noticed this morning that today is the 410th anniversary of Fermat's birth. We all remember from high school geometry that the sum of the squares of the sides of a right trangle equals the sum of the hypotenuse, or a2 + b2 = c2, the Pythagorean theorem. Fermat famously came up with his 'last theorem', that this did not work for other powers, e.g. there are no positive integers that lead to a3 + b3 = c3. Unfortunately he didn't have space in the margin where he noted to give the proof. Or maybe that was fortunate, as it inspired the last few centuries of mathematicians to tackle this problem, until it was finally proven in 1995. I couldn't find any LEGO creations relevant to Fermat, but the Pythagorean theorem is useful in building with LEGO. You may think that LEGO is limited to square structures, but using pythagoras you can connect things at other angles, using 3/4/5 triangles, or 5/12/13, etc. For example:

Or you can see the lines here:

The late Erik Brok did some work on this using hinges:

and technic beams:

There's more discussion of how to use Pythagoras in LEGO building on various LEGO sites, like here, here and . Break away from the rigid rules of right angles!

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