# MatheMatics Simulation

## Koch Curve

Koch curve Koch curve is a kind of fractal curve. It appeared in a 1904 paper titled ‘On a Continuous Curve Without Tangents, Constructible from Elementary Geometry’ by the Swedish mathematician Helge von Koch. Suppose there is a case in...

## Pythagoras Tree

The Pythagoras tree is a plane fractal constructed from squares. Invented by the Dutch mathematics teacher Albert E. Bosman in 1942. It is named after the ancient Greek mathematician Pythagoras. Fractal’s self-similarity Fractal curves retain their original shape even if...

## Pascal’s Triangle

Pascal’s triangle is a triangular array of the binomial coefficients. Each number is the sum of the two numbers directly above it. Pascal’s triangle has many properties and contains many patterns of numbers. The sum of the elements of row...

## Sierpinski Triangle

Sierpinski triangle is a fractal and attractive fixed set with the overall shape of an equilateral triangle. In this simulation, Create a Sierpinski triangle by endlessly drawing circles.

## C Curve

The C curve is a kind of fractal geometry. Bend each side 90 degrees. Bend this side again 90 degrees. Repeating this operation infinitely can get a C curve. Fractal’s self-similarity Fractal curves retain their original shape even if they...

## Dragon Curve

A dragon curve is a piece of paper folded several times in the same direction as the picture and then bent vertically. This curve does not intersect even though it may touch. As the number of folds increases, it becomes...

## Hilbert Curve

A Hilbert curve is a continuous fractal space-filling curve first described by the German mathematician David Hilbert in 1891. Fractal’s self-similarity Fractal curves retain their original shape even if they are greatly enlarged. Most fractal curves produce the same transformation...

## Sierpinski Curve

Sierpiński curves are a recursively defined sequence of continuous closed plane fractal curves discovered by Wacław Sierpiński. Fractal’s self-similarity Fractal curves retain their original shape even if they are greatly enlarged. Most fractal curves produce the same transformation over and...

## Epicycloid

Epicycloid refers to the trajectory drawn by a vertex on a small circle when a small circle is rolled outside a large circle. The radius of a large circle is denoted by R, the radius of a small circle is...

## Trigonometric functions

Definition of Trigonometric Functions In the right triangle, The longest side of the right triangle ‘c’ is the hypotenuse, ‘a’ is the base and ‘b’ is the height. You can assume that the angle between a and c is θ....

## Sum of Exterior Angle

Polygonal Exterior Angle Imagine drawing a polygon with a pencil. While drawing a straight line with a pencil, We change the direction at the vertex. The size of the angle changing direction at the vertex becomes ‘exterior angle.’ If you...

## Circumference of a Circle

How to find out the circumference of a circle Let’s draw a regular polygon (inscribed polygon and circumscribed polygon) surrounding a circle. The perimeter of an inscribed polygon is less than the perimeter of the circle, and the perimeter of...