Greenwood press

PROPORTIONS
85

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length. If the original ratio
surface area
volume
=
s
v
for the ant, the giant version 20 times 
bigger in each dimension would have 
surface area
volume
=
400 s
8000 v
. Hence the relative 
strength of a giant ant would be only 
400
8000
or 5 percent as much as a tiny ant. For
example, if a regular ant can carry ten times its body weight, then a giant ant
could only carry one-half its body weight. If such a giant ant existed, it would
probably have slightly different proportions than the smaller ant, since the cross-
sectional area of its legs would probably need to be proportionally larger in order
to maintain a dramatic increase in mass. Otherwise, there would be close to 90
times (20
3/2
) as much pressure on its legs than before, which would probably
cause the legs to snap. Ouch! That is why elephants need tree-trunk-style legs in
order to support their own weight. This proportional understanding of strength
helps designers build stronger paper towels, bags, and boxes, and helps engineers
build stronger and more durable machines that can withstand pressure such as
airplanes and bridges.
online references for further exploration
Eratosthenes of Cyrene

Build a solar system

Circumference of earth using techniques by Eratosthenes


Earned Run Average all-time leaders


Nuclear medicine

Orbit simulation

Map making


Proportional representation in voting


Scale models
 


Understanding scale speed in model airplanes

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