Visual Calculus

Mamikon A. Mnatsakanian (Armenian: Մամիկոն Մնացականյան) devised in 1959 a visual method to show that the areas of two annuli with the same chord length are the same regardless of inner and outer radii.
Annuli area
As an undergraduate, Mamikon specialized in the development of geometric methods for solving calculus problems by a visual approach that makes no use of formulas, which he later developed into his system of visual calculus.

Toeplitz’ Conjecture

Does every simple closed curve in the plane contain the vertices of a square?
No one knows, but the answer to this question is positive if the curve is sufficiently regular.
Toeplitz conjecture
The black dashed curve goes through all corners of several green squares.