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wu :: forums    riddles    easy (Moderators: ThudnBlunder, towr, Icarus, Eigenray, Grimbal, william wu, SMQ)    Pythagorean Proof « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Pythagorean Proof  (Read 380 times) Benoit_Mandelbrot Junior Member Almost doesn't count.     Gender: Posts: 133 Pythagorean Proof   « on: Mar 12th, 2004, 9:23am » Quote Modify This is another easy one, but here it is:   Prove the pythagorean theorem.  There can be more than one way to prove it. IP Logged Because of modulo, different bases, and significant digits, all numbers equal each other! Sir Col Uberpuzzler impudens simia et macrologus profundus fabulae     Gender: Posts: 1825 Re: Pythagorean Proof   « Reply #1 on: Mar 12th, 2004, 9:40am » Quote Modify How about forty-three different ways?     http://www.cut-the-knot.org/pythagoras/index.shtml IP Logged mathschallenge.net / projecteuler.net Benoit_Mandelbrot Junior Member Almost doesn't count.     Gender: Posts: 133 Re: Pythagorean Proof   « Reply #2 on: Mar 12th, 2004, 10:04am » Quote Modify Pretty much the only way I prove it is by similiar triangles, by having a line from the right angle of the big triangle perpindicular to the hypotenuse.  The hypotenuse becomes c=x+y.  We have a/c=x/a, and b/c=y/a.  We solve both for x and y, and add x+y.  We set this as c, and we come up with a2+b2=c2. IP Logged Because of modulo, different bases, and significant digits, all numbers equal each other! Sameer Uberpuzzler Pie = pi * e     Gender: Posts: 1261 Re: Pythagorean Proof   « Reply #3 on: Mar 12th, 2004, 11:14am » Quote Modify I will add some more ...     1) Right angled triangle ABC with AB=a,BC=b and AC=c   sinC=a/c and cosC=b/c sin2C+cos2C=1 a2+b2=c2   2) Consider a point (x,y) on the plane. If you drop a perpendicular on X axis then height = y and horizontal distance from Y axis = x By distance formula distance of that point from origin is sqrt(a2+b2) = c(lets say) Hence the Pythagoras identity follows IP Logged "Obvious" is the most dangerous word in mathematics. --Bell, Eric Temple Proof is an idol before which the mathematician tortures himself. Sir Arthur Eddington, quoted in Bridges to Infinity Sir Col Uberpuzzler impudens simia et macrologus profundus fabulae     Gender: Posts: 1825 Re: Pythagorean Proof   « Reply #4 on: Mar 12th, 2004, 12:35pm » Quote Modify *ahem* And where does the identity sin2C+cos2C=1 and the distance formula come from?   B_M, I think you meant b/c=y/b. IP Logged mathschallenge.net / projecteuler.net rmsgrey Uberpuzzler     Gender: Posts: 2873 Re: Pythagorean Proof   « Reply #5 on: Mar 12th, 2004, 12:39pm » Quote Modify My personal favourite is #9 on Sir Col's link. IP Logged Sameer Uberpuzzler Pie = pi * e     Gender: Posts: 1261 Re: Pythagorean Proof   « Reply #6 on: Mar 12th, 2004, 1:06pm » Quote Modify on Mar 12th, 2004, 12:35pm, Sir Col wrote: *ahem* And where does the identity sin2C+cos2C=1 and the distance formula come from?   LOL but the world is round   IP Logged "Obvious" is the most dangerous word in mathematics. --Bell, Eric Temple Proof is an idol before which the mathematician tortures himself. Sir Arthur Eddington, quoted in Bridges to Infinity Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------=> easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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