# Math Problems

A collection of math problems meant to illustrate the heart of mathematics. Each problem is linked to a page that discusses its solution, and the components required to understand it. These problems are meant to address ideas that have motivated different areas of mathematics.

## Problems

This page explains how to approximate the value of the square root of two using a recursive formula. The formula is explained and derived using algebra.

This video shows how to divide an angle into two equal parts using a compass and straight edge.

This video shows how to divide a line into two equal parts using a compass and striaght edge.

How to find the distance between two points using pythagorean's theorem.

To calculate pi geometrically we can use the perimeter of a polygon to approximate the circumference of a circle. This combined with the definition of pi, circumference divided by diameter, allows us to calculate a value for pi.

Riemann Sum is a method for approximating the area underneath a continuous function. To find the Riemann's sum, divide the area under the curve into n equal width rectangles. Then calculate the area of each rectangle and sum the results together.

This page explains how to draw a bezier curve using a ruler.

This video shows how to construct an ellipse using two tacks, a string, and pencil.

This video shows how to construct an equilateral triangle using a compass and straight edge.

This video shows how to construct a golden rectangle using a compass and straight edge.

To convert degrees to radians, multiply the angle by pi and then divide by 180.

To convert a point from the Polar Coordinate System to the Cartesian Coordinate System you can use the definition of sine and cosine to solve for the x and y component of the corresponding point.

To convert an angle from radians to degrees divide by pi and then multiply by 180.

How to find the equation of a circle that passes through three points.

This page describes how to find the line tangent to a curve at a point.

This page explains how to find the equation of the line that passes through two points.

This page explains how to find the point where two lines intersect.