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− | Most of us are familiar with triangular numbers, such as the arrangement of ten bowling pins in a triangle,
| + | #REDIRECT [[Activities/TurtleArt/Tutorials/Figurate_Numbers]] |
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− | or square numbers,
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− | but we don't necessarily know how their arithmetic works, or whether we can do the same with, say, pentagons.
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− | Can we learn something by telling a turtle how to make these numbers? Let's try.
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− | ==Linear numbers==
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− | 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.
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− | 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.
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− | [[File:TACounting.png]]
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− | ==Triangles==
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− | 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.
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− | [[File:TATriangularNumbers.png]]
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− | [[File:TATriangularNumbersProgram.png]]
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− | 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.
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− | [[File:TATriangularNumberFormulaHint.png]]
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− | 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?
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