Academic journal article The Science Teacher

Try This Tops Idea!

Academic journal article The Science Teacher

Try This Tops Idea!

Article excerpt

millimeter beads

...adapted from PI IN THE SKY#45

by TOPS Learning Systems

1. Count the mm beads in this circle to find its radius (R), diameter (D), and circumference (C). 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?

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

OBJECTIVE

To understand the geometry of circles, and how astronomers calculate apparent angular size.

MODEL ANSWERS

1. R = 35 mm; D = 70 mm. C = 220 mm. D fits into C [pi] times! ([pi] = 3 1/7 = 22/7 = 3.14). R fits into C 2[pi] times.

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

3. angular size = V35 radius of arc (1/35 rad) (180[degrees] / [pi] rad) = 1.64[degrees]

4. angular size = 1/110 radian (1/110 rad) (180[degrees] / [pi] rad) = 0. …

Search by... Author
Show... All Results Primary Sources Peer-reviewed

Oops!

An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.