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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Tilings, Platonic Solids, and Theorems

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Making Use of Linear Equations

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Angles and Pencil-Turning Mysteries

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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

Explore the beautiful and mysterious world of fractals. Learn what they are and how to create them. Examine famous examples such as Sierpinski's Triangle and the Koch Snowflake. Then, uncover how fractals appear in nature--from the structure of sea sponges to the walls of our small intestines.

The Pythagorean Theorem

We commonly define the Pythagorean theorem using the formula a2 + b2 = c2. But Pythagoras himself would have been confused by that. Explore how this famous theorem can be explained using common geometric shapes (no fancy algebra required), and how it's a critical foundation for the rest of geometry.

More with Less, Something for Nothing

Many puzzles are optimization problems in disguise. Discover that nature often reveals shortcuts to the solutions. See how light, bubbles, balloons, and other phenomena provide powerful hints to these conundrums. Close with the surprising answer to the Kakeya needle problem to determine the space required to turn a needle completely…

The Joy of Algebra

Arguably the most important area of mathematics, algebra introduces the powerful idea of using an abstract variable to represent an unknown quantity. This lecture demonstrates algebra's golden rule: Do unto one side of an equation as you do unto the other.

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