# Mathematics Simulation

## 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...

## 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...

## 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....

## Differentiation

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...

## Triangle and Tetragon

Triangle Regular Triangle The lengths of the three sides and the angles are the same. The size of each of the three angles is 60 °. It is the only triangle in which the inner center, circumcenter, and center of...

Degree ‘Degree’ is one of the units for measuring angles. When rotated one turn, it becomes 360 degrees. ‘Degree’ is the most commonly used unit. Radian ‘Radian’ is the ratio (= l / r) of arc length (l) divided by...

## Pythagorean Theorem 2

Pythagorean Theorem When the three sides of a right triangle are a, b, and c, and the longest side is c, the following equation is always true. The areas of a square with sides a, b, and c is a...

## Geometric Series

Geometric sequence is The geometric sequence is a sequence in which each term has a constant(common) ratio to its preceding term. For example, the geometric sequence with the first term ‘a’ and the common ratio ‘r’ is as follows. \[...

## Fourier Series 2

Fourier series The Fourier series is an infinite series that expresses a periodic function that repeats a certain part as the sum of simple trigonometric functions. A simple trigonometric function consists of a smooth surface wave. If you keep adding...