Greenwood press

PROPORTIONS
83
Congruent angles formed by the
sun’s rays at Cyrene and at the
center of earth. Note that figure is
not drawn to scale.
Movie screens are designed to be
in a similar proportion as the
dimensions of film cells.

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length of one of its edges raised to the third power. The ratio is used to find the
volume of the actual dinosaur, since the other measurements can be taken from
a model and a fossil of the skeleton. (See Similarity for an example.) The den-
sity of an object is the ratio of its mass to volume, so the mass of the dinosaur
can be predicted by estimating the density of a dinosaur as that of a modern-day
reptile or mammal.
The population of wildlife animals is determined by tagging animals and using
proportions. It is important to know these populations in order to understand if a
species is at risk of endangerment, or if there is an overpopulation that is affecting
an ecosystem. Every animal in a region cannot be counted, because it would be too
difficult to find all of them, not to mention that it would be distracting and poten-
tially disturbing to the ecosystem if ecologists were constantly roaming around.
Consequently, a scientist will go to an area such as a forest and temporarily cap-
ture animals to tag them. In addition to placing tags on them, the scientist will
likely examine their health to understand their potential to reproduce or spread dis-
ease. A few weeks later, after the animals have had a chance to roam around the
forest, the scientists will recapture a group of animals again to check their health
and keep track of the proportion of animals that are tagged. This information will
help the scientists determine how many animals are in that region of the forest,
assuming that the birthrate and death rate are fairly similar during that time period.
This method of estimating animal populations is called capture–recapture.
For example, suppose 50 deer are captured and tagged in a forest. Two weeks
later, 100 deer are captured, and 18 of them have tags. The proportion 
number of tags in population
number of tags in second sample
=
number of deer in population
number of deer in second sample
can be used to predict the total number of deer in that region of the forest. In this
case, the number of deer in the population, 
p, is approximately 277 based on a 
solution to the equation 
50
18
=
p
100
.