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 … more
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.
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 … more
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 … more
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 … more
Multiple Reflections
What is an image? Our eyes are designed to sense where the light came from. Even if the light didn’t actually originate there, if our eyes feel that way, our eyes say there’s an image there. … more
Graph of Saturated Vapor 2
Water vapor in the air Liquid water can evaporate and turn into water vapor in the air. Conversely, water vapor in the air may turn back into the water. Some are very dry, with no moisture … more
Convection
Convection When you boil water in the kettle, even if you heat only the bottom, the whole water becomes evenly hot. This is because water transfers heat while moving directly. In this way, liquid or gaseous … more
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 … more
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 … more
A Spaceship without Deceleration Engine
The inertia of the rocket Since there is no friction in outer space, stopping a rocket’s engine in motion does not stop it immediately. When the rocket’s engine is stopped, the rocket continues to move forward … more