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Unknown Measures of Similar Figures

Use ratios and proportions to solve for missing lengths in similar figures.

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Mighty Measurements

Credit: Guillaume Rouille
Source: http://commons.wikimedia.org/wiki/File:Thales_of_Miletus.jpg
License: CC BY-NC 3.0

Have you ever heard of Thales of Miletus? Born in 624 BCE, he was a Greek philosopher and mathematician who used indirect measurement to figure out the height of the Great Pyramid of Giza in Egypt. Do you have an idea of how he managed to do this?

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Around 2,600 years ago, Thales of Miletus discovered that the shadows cast by the towering pyramids in Egypt were in proportion to his own shadow. With this realization, he saw that he could determine the height of the Great Pyramid if he worked with similar triangles.

Credit: Francisco Anzola
Source: http://www.flickr.com/photos/fran001/2347859542/
License: CC BY-NC 3.0

He used the following proportion to figure out the height of the Great Pyramid:

man heightman shadow=pyramid heightpyramid shadow

By solving this proportion, Thales went on to prove that with indirect measurement, humans were capable of measuring colossal objects, regardless of their height.

See for yourself: http://www.youtube.com/watch?v=ozlggIEXCoQ

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Watch the first video to learn more about the accomplishments of Thales of Miletus. Watch the next clip to further explore indirect measurement.

http://www.youtube.com/watch?v=eMkNu0d3ae0

http://www.youtube.com/watch?v=aMiKNToaQ0k

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Image Attributions

  1. [1]^ Credit: Guillaume Rouille; Source: http://commons.wikimedia.org/wiki/File:Thales_of_Miletus.jpg; License: CC BY-NC 3.0
  2. [2]^ Credit: Francisco Anzola; Source: http://www.flickr.com/photos/fran001/2347859542/; License: CC BY-NC 3.0

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