All Triangles are Equilateral - Numberphile
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users link it when discussing false proofs, especially the "all triangles are equilateral/isosceles" fallacy and where its hidden error lies.
Recommended by 1 people across 1 different months, 2014 to 2015.
What it is
A five-minute Numberphile video in which Carlo Séquin presents the classic fake proof that every triangle is equilateral, then invites viewers to find the flaw. It is a short geometry puzzle built around a perpendicular bisector and an angle bisector meeting at a point.
What people said
Recommends Barry Cipra · 2015-10 · Mathematics Stack Exchange · on “What are some false proofs for true or false statements where the error in the proof is not obvious?”
There is a famous old "proof" that all triangles are equilateral. I first came across it in Harold Stark's An Introduction to Number Theory (pp. 223-224). Carlo Sèquin gives a nice, five-minute [this video] of it.
Cites dietervdf · 2014-11 · Mathematics Stack Exchange · on “Geometry: perpendicular bisector and bisector unknown theorem”
Inspired by one of the latest [this video] numberphile videos I started playing around with the specific configuration. I would like to prove the following: Given is a random $\triangle ABC$ with perpendicular bisector $MS$ and bisector $AS$ . (see figure) If $\widehat{SBA} > 90°$ then $\widehat{ACS} < 90°$ Experimenting in Geogebra gave me some clues. If I could prove $\widehat{BAS} = \widehat{SBM}$ (which is quite surprising) then proving the conjecture above would be a breeze. However this task seems quite challenging, I tried proving $\triangle BMS \sim \triangle AHS$ without success. Could someone give me some pointers? (Is this a known theorem?)
Cites arunoruto · 2015-01 · Mathematics Stack Exchange · on “All triangles are equilateral”
So I was watching a video in which a man has "proven" that all triangles are equilateral. He also said that there is somewhere an error but I really cant find. So can someone show me it or give me a hint. The video: [this video] What I noticed is that if AB=AC then AX and AM are the same line and cant intersect.
Cites user3875728 · 2015-09 · Mathematics Stack Exchange · on “What is the flaw in this proof that all triangles are isosceles?”
First off, the other two answers here are wrong because you can prove the statement using the same flaw if P was outside the triangle. The proof using the same flaw but done in the outside of the triangle is here: [ [this video] The video clearly does this proof with P on the outside. If P were on the segments of the triangle, then the proof will still hold because triangle AEP will be congruent to triangle AFP by SAA (shared sides, bisected angles, 90 degree angles). You know that P and D are the same points because the definition of P is where the perpendicular bisector meets the bisector of the opposite angle, and provided the case where P's on BC, it can only possibly be a triangle if P and D