Boat Puzzle: Missionaries and Cannibals
Both missionaries and cannibals must cross the river safely. Boats can ride up to three people. If the number of cannibals is more than the number of missionaries anywhere, missionaries will be eaten.
Distance and Displacement
Distance One of the most used concepts is ‘distance,’ which means the total distance actually moved. If you move in zigzag, the actual distance traveled can be quite long, even if the straight distance is short. … more
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 … more
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 … more
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