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LionJim

LionJim

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Oct 12, 2021
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There are two types of irrational numbers: algebraic irrationals and transcendental numbers (which are always irrational). An algebraic number is a real number which is a root of a polynomial with integer coefficients. The number sqrt(2) is irrational (the proof of this predates Euclid) and is algebraic because when you plug it into the polynomial f(x) = x^2 - 2 you end up with zero. A real number which is not algebraic is said to be transcendental. Lambert proved in 1761 that pi is irrational, but it wasn’t until 1882 that Lindemann proved that pi is transcendental. Proving pi is transcendental was a big deal (much bigger a deal than being irrational) because it proved that you can’t construct a segment of length pi with a straightedge and compass; pi, being transcendental, is not constructible. (Although not every algebraic number is constructible, sqrt(2) is constructible as it is the hypotenuse of an isosceles right triangle with legs of unit length.)

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Squaring the circle - Wikipedia

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Woodpecker

Woodpecker

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s1uggo72 said:
that always reminds me of MIT fight song
e^x E^xdx
e^x e^xdx
secant tangent cosine sine
3.14159
Click to expand...
Go team,
Hit 'em with a log!
 
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