Academic journal article The Science Teacher

Millimeter Beads: ... Adapted from PI IN THE SKY#45 by Tops Learning Systems

Academic journal article The Science Teacher

Millimeter Beads: ... Adapted from PI IN THE SKY#45 by Tops Learning Systems

Article excerpt

1. Count the mm beads to find the radius (R), diameter (D), and circumference (C) of this circle. How many D's fit around C? How many R's?

2. Argue that 180[degrees] = [pi] radians.

3. If the moon were 35 moon-diameters from Earth, what would be its apparent angular size in radians? In degrees?

Each tiny bead is one millimeter in diameter.

4. Our moon is actually 110 moon-diameters away. What tiny angle does it subtend in your field of view?

[c] 2008 by TOPS Learning Systems. Photocopies permitted if this notice appears. All rights reserved.

OBJECTIVE

MODEL ANSWERS

1. R = 35mm;D = 70mm.C = 220 mm. DfitsintoC^times!(^ = 3 V> = 2^ = 3.14). Rfits intoC27r times.

2. Students might draw 3 one-radian angles, observing that they fall 5 beads short of 180[degrees]: 3 5/35 rad = 3 1/7rad = [pi] rrad = 180[degrees]

3. angularsize = 1/35 radius of arc (1/35 rad) (180[degrees]/[pi] rad) = 1.64[degrees]

4. …

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