Is every triangle a rep-4 tile?

Is every triangle a rep-4 tile?

All triangles and parallelograms are rep-4 tiles. Besides these obvious examples, a great number of rep- tiles are known.

What is a tiling in math?

A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern.

Is every rectangle A rep 2 tile?

“Rep-tile” has a different meaning in Mathematics It is short for Replicating Tile. When several copies of these tiles are put together, the shape will appear exactly the same but magnified! Every square, rectangle, parallelogram, rhombus, or triangle are examples of rep-tiles.

Is a scalene triangle A rep-tile?

Mathematicians have shown that any triangle and any parallelogram is a rep-4 tile. In other words, four copies of a triangle or a parallelogram create a larger similar triangle or parallelogram.

What shapes are Rep tiles?

Some rep-tiles are based on polyforms like polyiamonds and polyominoes, or shapes created by laying equilateral triangles and squares edge-to-edge.

• Squares.
• Equilateral triangles.
• Right triangles.
• Rep-tiles as fractals.
• Fractals as rep-tiles.
• Rep-tiles.
• Irrep-tiles.

Is Hexagon a rep tile?

It is commonly known that any triangle, quadrilateral, and regular hexagon will tile the plane. A rep-tile tiles the plane. Another way that one can think of a rep-tile is as a puzzle piece, where a larger similar figure is the entire puzzle.

What’s the tile?

The Tile location system uses BLE to connect to devices – all it needs is Bluetooth and some battery life. When a device is in range, you can simply open the app on your phone, tap the Tile and find it – the Tile then plays a tune so you can locate it.

Is Hexagon a rep-tile?

Are all triangles Rep tiles?

Every square, rectangle, parallelogram, rhombus, or triangle is rep-4. A rectangle (or parallelogram) is rep-n if its aspect ratio is √n:1. An isosceles right triangle is also rep-2.

What is a rep tile in geometry?

In the geometry of tessellations, a rep-tile or reptile is a shape that can be dissected into smaller copies of the same shape. The term was coined as a pun on animal reptiles by recreational mathematician Solomon W. Golomb and popularized by Martin Gardner in his ” Mathematical Games ” column in the May 1963 issue of Scientific American.

What are rep tiles used for in fractals?

Rep-tiles as fractals. Rep-tiles can be used to create fractals, or shapes that are self-similar at smaller and smaller scales. A rep-tile fractal is formed by subdividing the rep-tile, removing one or more copies of the subdivided shape, and then continuing recursively.

What is a rep-tile dissection?

A rep-tile is labelled rep- n if the dissection uses n copies. Such a shape necessarily forms the prototile for a tiling of the plane, in many cases an aperiodic tiling. A rep-tile dissection using different sizes of the original shape is called an irregular rep-tile or irreptile.

How many rep-tiles are there and how many are there?

An infinite number of them are rep-tiles. Indeed, the simplest of all rep-tiles is a single isosceles right triangle. It is rep-2 when divided by a single line bisecting the right angle to the hypotenuse. Rep-2 rep-tiles are also rep-2 n and the rep-4,8,16+ triangles yield further rep-tiles.