In mathematics, it seems that when we try to find relations about objects we are forced to set a unique object as a basis for the construction of each other object. For example: take one rectangle and define It's area as b•h, now if you take a line through Its center, it will allow you to cut the rectangle in two having its area divided in two pieces (b•h/2). Now if you rotate the line in a way that it passes through two vertices of the rectangle, then you have a triangle and it has the same area: (b•h/2).

Now for the area of the circle, we need to make a comparison between what we made and we can do that by inscribing a regular polygon and taking the limit of its sides to infinity, that is: it's measure will depend on the sum of a infinity of triangles. Even in integral calculus, the area under the curves is defined as the sum of an infinity of rectangles, consequently: An infinity of triangles. And hence, the triangle seems to be the most basic object found when building these relations.

Does this effect have a name? Has someone written about it? If yes, who?

  • Which effect? The construction using geometry, the use of limits as a number of sides approaches infinity, or the fact that triangles "seem to be most basic"? I presume the middle one is the focus of the question, but I wanted to ask. – Cort Ammon Nov 18 '15 at 20:43
  • It's the last one. – Billy Rubina Nov 19 '15 at 1:40

Exhausting plane geometric figures by triangles is named triangulation.

In dimensions higher than two, i.e. for not necessary plane figures, the generalisation of triangles is named simplices. This leads to the mathematical concept of homology, which in the 20th century developed into Algebraic Topology.

| improve this answer | |
  • I know,but that's not my point. – Billy Rubina Nov 19 '15 at 1:40

Insofar as I understand your question, are you perhaps looking for the category-theoretic concept of "universal property"?

| improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.