International Journal of Mathematics and Mathematical Sciences / 2012 / Article / Fig 1

Research Article

A New Proof of the Pythagorean Theorem and Its Application to Element Decompositions in Topological Algebras

Figure 1

Diagram relating to proof that the function giving the length of a line segment with one endpoint at has continuous directional derivatives at points other than , Lemma 2.3. Three facts used in the proof are as follows: (1) is similar to because is a right angle, (2) for all , the triangles are similar, (3) is between and .