Math: how far away is the goose?

Tutoring math, you notice that people like relatable examples. The tutor brings up his observation of a Canada goose.

Looking out over a lake in Nanaimo on Sunday morning, I saw an exceptional Canada goose swimming apart from the others.

The setting was so tranquil, even distance seemed irrelevant: I felt that, on a whim, I could suddenly scoot down to the water, plunge in, and join the goose if I wanted. Yet, how far away was it, really?

Holding my phone at 20cm, or 200mm, I observed the goose at about one-sixth of my phone’s lens port, which is 7mm across. So, to me, the goose appeared 7/6=1.17mm. Yet, a goose that prosperous would likely be about 60cm, or 600mm, from tail to breast. From optics,

object distance/image distance = object length/image length


d/200 = 600/1.17

Multiplying both sides by 200, we get

d=200(600)/1.17 = 102574mm or about 103m


Bull, John and John Farrand, Jr. The Audubon Society Field Guide to North American Birds, eastern region. New York: Alfred A. Knopf, 1977.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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