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Somehow, the "original proof" seems simpler. > The first rigorous proof that π is irrational is from Johann Heinrich Lambert in 1761. He proved that if x≠0 is
by hasenj 11y ago
Somehow, the "original proof" seems simpler.
> The first rigorous proof that π is irrational is from Johann Heinrich Lambert in 1761. He proved that if x≠0 is rational, then tan(x) must be irrational. Since tan(π/4)=1 is rational, then π must be irrational.
Of course, the proof for (tan(x) is irrational for rational x != 0) might be complicated, but at least it's easy to see why this proves that PI is irrational.
This one, on the other hand, I can't even follow in principle what it's trying to say.
That's of course because I don't understand integrals and differentials.
- jordigh 11y agoThat just wraps up a mystery inside another. Why would tan(x) be irrational if x is rational? That seems like an even bigger mystery than why π is irrational.
- dnautics 11y agoThats easy if you remember arctan(y/x) is the angle from x axis to (x,y)
- hebdo 11y agoI fail to see how this helps. Actual proof is more complicated, it is based on continued fractions.
- hasenj 11y agoIt's all mysteries. The point of "simple" is to create a series of simple steps, each step should be straight forward and easy to understand. Terse != simple
- hebdo 11y ago> Of course, the proof for (tan(x) is irrational for rational x != 0) might be complicated It is: http://www.pi314.net/eng/lambert.php http://www.pi314.net/eng/lambert.php