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Add examples to stub
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.
==Linear numbers==
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.
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.
[[File:TACounting.png]]
==Triangles==
What should we add? How about making dots of different colors, and providing notes about how many of each, plus the running total? Easy-peasy. We just need to do the arithmetic to work out where to put everything.
[[File:TATriangularNumbers.png]]
[[File:TATriangularNumbersProgram.png]]
A problem that TA can't solve for us directly is the formula for triangular numbers. Gauss figured it out on his own as a child, but the rest of us need a hint, at least. Here is a big hint.
[[File:TATriangularNumberFormulaHint.png]]
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?