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.
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.