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but we don't necessarily know how their arithmetic works, or whether we can do the same with, say, pentagons.
but we don't necessarily know how their arithmetic works, or whether we can do the same with, say, pentagons. Pythogoras, the founder of Greek mathematics, is said to have discussed these figures and their relationships. We know that the triangle of 10 points, called the tetractys in Greek, was a central element in the Pythagorean religion.
Can we learn something by telling a turtle how to make these numbers? Let's try.
Can we learn something by telling a turtle how to make these numbers? Let's try.
Before we get to triangles, squares, and so on, we need to have a few tools, such as those provided in the [[Activities/TurtleArt/Tutorials/Counting|Counting]] tutorial, so that we can create figures and post notes about them. Then we can add a few more things.
Before we get to triangles, squares, and so on, we need to have a few tools, such as those provided in the [[Activities/TurtleArt/Tutorials/Counting|Counting]] tutorial, so that we can create figures and post notes about them. Then we can add a few more things.
==Triangles==
==Triangles==
The area of a rectangle can be written Base × Height. The area of a right triangle is half the area of a rectangle with the same Base and Height. Can you do the rest?
The area of a rectangle can be written Base × Height. The area of a right triangle is half the area of a rectangle with the same Base and Height. Can you do the rest?
==Other Figurate Numbers==
Two-sided polygons may or may not be allowed in a particular geometry, but they are not of interest here, because both sides are necessarily of the same length in Euclidean geometry and Lobachevskian/hyperbolic geometry, and of indeterminate length in Riemannian/elliptic geometry, rather like cutting a great circle on a sphere into two pieces.
[[File:TACounting.png]]
We need separate pages for each of the remaining topics. Here you go.
* [[Activities/TurtleArt/Tutorials/Square_Numbers|Square Numbers]]
* [[Activities/TurtleArt/Tutorials/|Pentagonal Numbers]]
* [[Activities/TurtleArt/Tutorials/Pyramidal_Numbers|Pyramidal Numbers]]
* [[Activities/TurtleArt/Tutorials/Cubic_Numbers|Cubic Numbers]]