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**Feature Article: Measures**

As pilots we are,
generally unaware and/or uneducated, as to the debt that aviation
owes to those scientists and mathematicians who preceded the Wright
brothers. The mathematics of aviation begins with the prehistoric
use of our hands which gave us the span as in wingspan.

Consider the beginning the numbering system. The Babylonians,
over 6000 years ago, added the use of symbols, `zero', and place
value to make mathematics possible. From the Babylonians we acquired
the Base 60 numerical system used in telling time. This base sixty
is also part of our navigational system. Ever notice how easy
it is to do fractions in Base 60.

It is interesting to note that the sum-of-the-digits for every
45-degrees all around the compass rose is the same. This is true
no matter where we start on the rose.

360 = 9; 270 = 9; 090 = 9; 135 = 9

The Egyptians, not
much later, devised a way of dividing the year into twelve months
even including the leap year. They followed up with land measuring
systems not unlike those used in modern map making.

The Greeks developed axioms into theorems and proofs. They used
abstractions to illustrate the reality of the world. Such abstractions
pilots now call sectionals, charts, or maps. The Greek, Thales,
demonstrated five propositions which have become part of geometry
or earth measurement.

· A circle is bisected by its diameter. Whenever we
draw a course line we are bisecting a circle.

· Equilateral triangles
have equal sides and angles. Every time we make a 45 entry to
an airport, decide when to turn downwind and determine the `key'
point to turn base we are applying our knowledge of equilateral
triangles.

· A diagonal through parallel lines give equal opposite
angles

A knowledge applied
every time we enter on a 45 and enter downwind.

· Triangles having one side equal as well as two angles
equal are congruent.

Euclid also collected
all the math ideas he could such as all right angles are equal,
a straight line can be drawn from one point to another point,
and the sum of the angles in a triangle equal 180 degrees. Archimedes
was a mathematician as well as a creative engineer. He used a
screw shape in tube to move water. The movement of a propeller
through the air is such a screw. Early propellers were called
air screws. His use of pulleys and levers have applications in
aircraft control systems. Pythagoras with his followers discovered
the roundness of the earth, the numerical relationships of frequencies,
and the Pythagorean Theorem whose hypotenuse we fly during climbs
and descents.

WWII navigation with sextant, chronometer, almanac, all of which
made possible finding a line of position using the celestial method
of Marcq St.-Hilaaire. Radio navigation uses this method of a
line of position with intersecting lines for a given position
on the line. Only a timing device is required be it a watch or
DME.

Last Modified October 10, ©2024 TAGE.COM