The Epsilon-Delta Definitions of Limits

Andre Bautista — Wed, 21 Jul 2010 06:13:41 +0000

The concept of definition of limits is one of the most difficult concept to understand in elementary calculus. Salman Khan has an excellent explanation about it from Khan Academy. Khan’s videos are shown below.

Part I

Part II

Enjoy learning math!

Proof of the Pythagorean Theorem

Andre Bautista — Sun, 18 Jul 2010 11:09:42 +0000

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. This means that if the triangle has side lengths a, b and hypotenuse c, the following equation holds: c² = a² + b².

Right Triangle ABC

" data-medium-file="https://polymathcentral.wordpress.com/wp-content/uploads/2010/07/righttriangle.png?w=300" data-large-file="https://polymathcentral.wordpress.com/wp-content/uploads/2010/07/righttriangle.png?w=354" class="size-medium wp-image-6 " title="righttriangle" src="https://polymathcentral.wordpress.com/wp-content/uploads/2010/07/righttriangle.png?w=300&h=249" alt="" srcset="https://polymathcentral.wordpress.com/wp-content/uploads/2010/07/righttriangle.png?w=300 300w, https://polymathcentral.wordpress.com/wp-content/uploads/2010/07/righttriangle.png?w=210 210w, https://polymathcentral.wordpress.com/wp-content/uploads/2010/07/righttriangle.png?w=150 150w, https://polymathcentral.wordpress.com/wp-content/uploads/2010/07/righttriangle.png 354w" sizes="(max-width: 210px) 100vw, 210px" />

Right Triangle ABC

The proof of the theorem is shown below.

Proof of the Pythagorean Theorem

Looking at the diagram, does the equation above will always hold? Explain why.

Note: Image courtesy of Mathematics and Multimedia

Polymath Central

The Epsilon-Delta Definitions of Limits

Proof of the Pythagorean Theorem