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...
MatheMatics Simulation
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....
