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Addition Line Drawing Polygons Polyhedra

As a continuation of our parabolic and exponential curves created with line designs, we did exercises that required them to answer addition questions and then connect sums with the correct answers.

We also used this exercise to have them group answers withing a certain range. For example, if 78 + 12 = 90, we might have had them color all answers in the range of 81-100 red, and so on. This would have created a beautiful design with symmetry and patterns by color as well as checking their addition skills.

Line Drawing Parabolic Curves

Parabolic curves are not really curves at all but just a series of lines starting at the endpoint of an angle to one dot over from the vertex of the angle; the next line follows towards the vertex of the angle until it completes the "representation" of a curve.

It is much easier to follow the instructions on the attached pdf. I made it relatively easy by providing letters so the students could follow from A to A, B to B and so on.

Josephus Problem: Counting-off Puzzle

Reuleaux Polygons

Reuleaux polygons are shapes that have constant width just like a circle. In a circle, all diameters are of equal length. That is, all segments drawn through the circle's center are of constant length. This is why wheels have been used in transportation, machinery, energy and countless other uses for about 10,000 years. However, the earliest discovery of the wheel dates back to 3500 B.C. in Mesopotamia.

Construction of Circles, Regular Hexagons and Derivative Works

 

"Construction" in geometry means to draw shapes, angles or lines accurately.

These constructions use only compass, straightedge (i.e. ruler) and a pencil.