The main problem is that you say to 'Slowly scale (contract) the triangle down to a point.'īut what point? Scaling a triangle requires that you pick a point to scale it down to, and move the vertices towards that point at a uniform rate. I think it cleverly hides this, and seems to be possibly correct, but if you try to write down the details, you will not get anywhere with it. But others have not been honest enough: the idea of this proof is not correct. Please don't take this harshly - I think it's a very nice idea. Therefore, the three medians intersect at a point. The three corners of the triangle trace the three medians of the triangle. Proof: Slowly scale (contract) the triangle down to a point. However, in your example above, almost anyone could, because it's not quite watertight enough. The answer to that question, for a proper proof, is no. I won't provide you with a proof, that would ruin all your fun, but the main thing is to ask yourself 'If I say this to somebody, do they have any other choice than to agree with me?'. This is unfortunately tantamount to stating what you're trying to prove - and is a no no! You follow this up by asserting something about the corners tracing the three medians of the triangle. What does it mean to 'Slowly scale (contract) the triangle down to a point.'? Intuitively we do understand, but mathematically, we do not. The problem with your proof is that you don't actually define anything that you've said. Now time for the bad news unfortunately, intuition does not a mathematical proof make. Intuitively it does indeed seem that if you do as you say and 'contract' the triangle down to a point, the corners trace the medians, and eventually meet at a single point, or something like that. It seems you've got something of the right idea.

Well, since you've asked for criticism, here some is! (Both positive and negative).įirstly, nice try.

Construction of a median geometry