Session 2: Notes

A B C

Notes for Session 2, Part B

Note 8

If you are working in a group, work in pairs on Problem B3. Practice setting up proportions (two ratios that are equal to each other) to determine the length of the different body parts in your drawing.

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Note 9

This problem may take some time, especially if you are trying to use one scale for both the diameter of the planets and their distances from the Sun. Often, models are created that focus on one or the other (size vs. distance). If you choose a scale that allows distances from the Sun to fit into a large room, you will find that the models of some of the planets are very, very small. If you choose a scale that allows the models of the planets to be big enough that you can observe them, you will find that the distances between planets in the model must be very large.

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Note 10

To learn more about the Pythagorean theorem, go to Learning Math: Geometry, Session 6.

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Note 11

The is an irrational number, because it cannot be expressed as a fraction a/b, where a and b are integers and b 0. In other words, this value can't be written as a fraction or as a repeating or terminating decimal. If we expressed it as a decimal, it would have an infinite number of digits to the right of the decimal point in a non-repeating pattern. The real-number system is made up of an infinite number of rational numbers (those that fit the fraction property above) and an infinite number of irrational numbers. There are many situations where a length is actually an irrational number (such as the hypotenuses of isosceles right triangles), so we cannot measure the length exactly. The idea that a measure is always an approximate value is a hard one to grasp, since in everyday life we treat measures as exact quantities.

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Session 2 | Notes | Solutions | Video