# MatheMatics Simulation

## Hypocycloid

A hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. If the radius of a large circle is $$R$$, and the radius of a small...

## Hypocycloid 2

A hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. If the radius of a large circle is R, and the radius of a small...

## Polygonal Wheel

Polygon Wheel Should the wheels always be round? All polygon wheels can roll smoothly. To do this, you need a suitable floor. How is the floor for the polygonal wheel to roll smoothly? The floor shown in the above simulation...

## Integral in physics

Definite integral In the 2D coordinate plane, a definite integral is a way to find the area of a graph. In a rectangle, the only simple way to get the area is the multiplication of width and height. If the...

## Mandelbrot Set

This simulation supports both pinch zoom and mouse scrolling. We recommend using the Chrome browser. (to get more processing speed) Imaginary number An imaginary number consists of a number that becomes negative if you square itself. The letter ‘ i’...

## Differentiation 2

Differentiation The differentiation is to find the amount of change at a point on a graph f(x). This is like the process of finding the slope of the tangent line when you can draw a tangent at a point on...

## Voronoi Diagram Drawing

A Voronoi diagram is a partitioning of a plane into regions based on the distance to points in a specific subset of the plane. That point set is specified beforehand. And regions(Voronoi cells) are consisting of all points closer to...

## Voronoi Diagram

A Voronoi diagram is a partitioning of a plane into regions based on the distance to points in a specific subset of the plane. That point set is specified beforehand. And regions(Voronoi cells) are consisting of all points closer to...

## Lissajous Figures

The Lissajous figures The Lissajous figures is a planar shape drawn by the following equation by the parameter t: x = A cos (Bt + C)y = D sin (Et + F) If B:E is an integer ratio, you can...

## Triangle Trick

Triangle Trick If you look closely, you can see that the triangle’s slope is not a straight line. One of the merged triangles is slightly convex up, and the other is somewhat concave down. However, the convexity and concaveness are...

## Fourier Analysis

Fourier series A Fourier series is a way to represent a function as the sum of simple sine waves. A simple trigonometric function consists of a smooth surface. If you continue to add these trigonometric functions, you can get a...

## Ellipse

Ellipse An ellipse is a closed curve connecting the points that the sum of the two distances to the focal points is a constant. The ellipse’s longest diameter is the major axis, and the shortest diameter is the minor axis....