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# M5.4.12

Uses geometric models, diagrams, and graphs to solve real-world problems.

### How Big Is the Earth?

In collaboration with another school north or south of yours, rnuse the method of Eratoshenes to determine the circumference rnof the Earth.

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### Geometry to the Rescue: A Story in Pictures

Our kitchen floor was in need of something (repair, replacement, rejuvenation?). This being the do-it-yourself age, we took ourselves to the nearest big box home store, and picked out a lovely laminate flooring in a pattern that looks like tile. The ads and the instructions all make it sound like a pretty simple project. We brought it home and set to work. Immediately, we ran into a problem (Fig. 1). Our breakfast nook is in an octagonal shape. This means no matter which wall we started on, we immediately had to tackle an angle cut.

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### Determining the Altitude of Iridium Flares

If you have a clear night and you're somewhat removed from city lights, many satellites are fairly easy objects to see. They look like faint stars (occasionally bright stars) gliding across the night sky. Sometimes satellites look like airplanes, but airplanes have blinking lights that are usually colored. What's interesting about Iridium satellites, from a star gazing point of view, is that they can suddenly brighten and may easily outshine every star or planet in the sky.

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### Can an Astronaut on Mars distinguish the Earth from its Moon?

Some day an astronaut will stand on Mars and look back at Earth. As Alfred, Lord Tennyson wrote Venus, Hesper, Were we native to that splendour or in Mars We would see the globe we groan in, fairest of their evening stars Could we dream of wars and carnage, craft and madness lust and spite Roaring London, raving Paris, in that peaceful point of light? Would we not, when gazing heavenward, at a star so silver-fair Yearn, and clasp the hands, and murmur: Would to God that we were there? But what exactly will one see from Mars?

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