Episode 7 of Geometry

Examine how our usual definition of parallelism is impossible to check. Use the fundamental assumptions from the previous lectures to follow in Euclid's footsteps and create an alternative way of checking if lines are parallel. See how, using this result, it's possible to compute the circumference of the Earth just by using shadows!

Running Time

35 mins

Year

2014

Kanopy ID

1338401

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A Return to Parallelism

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Complex Numbers in Geometry

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--the guessing and…

The Joy of 9

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Visualizing Area Formulas

Never memorize an area formula again after you see these simple visual proofs for computing areas of rectangles, parallelograms, triangles, polygons in general, and circles. Then prove that for two polygons of the same area, you can dissect one into pieces that can be rearranged to form the other.

Similarity and Congruence

Define what it means for polygons to be "similar" or "congruent" by thinking about photocopies. Then use that to prove the third key assumption of geometry--the side-angle-side postulate--which lets you verify when triangles are similar. Thales of Ionia used this principle in 600 B.C.E. to impress the Egyptians by calculating…

The Mathematics of Fractals

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