- #TESSELLATION SQUARE AND OCTAGON HOW TO#
- #TESSELLATION SQUARE AND OCTAGON FULL#
- #TESSELLATION SQUARE AND OCTAGON CODE#
We need to make squares and polygons with sides the same length. After that you just cut and paste or work with the object.
#TESSELLATION SQUARE AND OCTAGON CODE#
You should only write a piece of code once. Real programmers work by creating objects and then joining those objects together.
#TESSELLATION SQUARE AND OCTAGON HOW TO#
Can you work out how to copy it so that it joins up without leaving gaps? Here is a pattern that will tile the plane.
The problem is that you can't join this pattern up without leaving gaps. This code fits 2 squares, a triangle and a hexagon around one vertex. (One vertex arrangement produces two distinct tilings. Only 7 of these can tile the plan without leaving gaps. There are actually 17 ways that you can fit polygons together around a vertex so that they total exactly 360 degrees. To find the other 7 patterns first find sets of polygons that can be joined together around one vertex without overlapping or leaving gaps. Each vertex must have the same number of the same type of polygon and the polygons must all have the same size side. You can also tile the plane by using combinations of regular polygons. Have you worked out what the other two shapes are?Ĭan you get them to join together and produce a tiling? Squares are easiest to use so do them first. Repeat 3 rt 90 fd 100 lt 90]įor a better way to do this and to find out how to colour the square in go to Advanced Options at the bottom of the page.Īpply what you have learned and tile the plane completely with patterns built up from one kind of regular polygon. I've also shrunk the squares so that they don't go off the screen. My program repeats the "squares around a vertex" bit three times. Then repeat the square drawing procedure.
#TESSELLATION SQUARE AND OCTAGON FULL#
You now need to move the turtle two full squares to the right and get it pointing upwards. To demonstrate this in Logo you need to be able to draw the polygons around one vertex and then move the turtle to the next vertex. You should now know the three regular polygons which can be used, on their own, to tile the plane completely. The problem is that they don't join up to make 360 degrees. It has drawn an octagon, a duodecagon and a triangle. Thr routine has been called three times here. The pv routine has drawn an octagon and then turned through 135 degrees. This one draws a particular polygon and then moves the turtle to the correct position for drawing another polygon that is joined onto the first one. Here are a few attempts that are deliberately wrong. To do this you are going to have to turn the turtle through the correct angle before drawing the next shape. You can now draw one polygon but you need to draw several that meet at a common point or vertex. This draws a hexagon with sides that are 60 pixels long.
Now click on the "file" menu and select "save and exit". I've used the "set" menu to alter the font. Now add the text that you can see in the picture. You can write a general polygon program as follows: The external angle of a polygon of n sides is 360/n This program draws an equilateral triangle. You should have done this before in previous Logo sessions. To do this you need to be able to draw a polygon Remember that regular polygons have equal sides and equal angles. Your first mission is to find the three ways of completely tiling a flat surface (plane) using only one kind of regular polygon Task 1 Tiling the plane with regular polygons. The hexagons' sides look bigger but aren't really. The hexagons and the equilateral triangles have sides that are the same size. A tessellation is an arrangement of tiles fitting exactly together which can be extended as far as required in any direction.
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