Tessellations are made by repeatedly overlapping a figure
Ah, tessellations! They're like puzzle pieces for mathematicians who prefer to make art instead of solving equations. It's like taking a shape and saying, "Hey, let's make a bunch of copies of this and see if we can arrange them in a way that covers a plane without any gaps or overlaps." It's the art of turning shapes into a stylish quilt, all snug and tidy. So, go on, overlap those figures and let the tessellation magic begin!
To understand and create a tessellation, you can follow these steps:
1. Start with a simple figure or shape. It can be any shape you like, such as a square, triangle, or hexagon.
2. Decide on the position and orientation of your initial figure. This will serve as the "tile" that will be repeated to form the tessellation.
3. Repeat the initial figure to fill the plane without any gaps or overlaps. You can do this by duplicating and translating the figure, ensuring that each repetition lines up with the previous one perfectly. This will create a pattern of overlapping shapes.
4. Continue duplicating and translating the figure until you have covered the entire plane. The goal is to create a design that fits together seamlessly.
5. You can experiment with different shapes and arrangements to create unique tessellations. Some common examples include regular tessellations with squares, triangles, or hexagons, as well as more complex patterns using irregular shapes.
It is important to note that not all figures can be used to create a tessellation. In order to tessellate, a figure must have sides that can fit together with no gaps or overlaps. Regular polygons (shapes with equal sides and angles) are usually the most effective for creating tessellations.
Tessellations are created by repeating a pattern or shape in a regular grid so that there are no gaps or overlaps between the shapes. Here are the steps to create a tessellation:
1. Choose a shape: Start by selecting a shape or pattern that you want to use. Common shapes for tessellations include triangles, squares, hexagons, and even irregular shapes.
2. Create the base: Begin by drawing a basic shape or pattern on a piece of paper. This will serve as the base for your tessellation.
3. Copy the base: Take your base shape and make copies of it, ensuring that each copy is adjacent to the previous one. You can create copies by tracing the shape or using a ruler and compass to recreate it.
4. Fill the plane: Continue copying and placing the shape until it fills the entire plane without any gaps or overlaps. The copies should fit together like puzzle pieces, forming a repeating pattern.
5. Explore variations: To make your tessellation more interesting, you can experiment with rotating, reflecting, or scaling the shapes as you copy them. This will create different effects and designs.
6. Color and decorate: Once you have completed the tessellation, you can add colors or decorations to make it visually appealing. This step is optional but can enhance the overall aesthetic of your design.
Remember, tessellations can be as simple or complex as you like, so feel free to get creative and experiment with different shapes, patterns, and variations.