Geometry:
The ancient Egyptians and Mesopotamians developed
methods of measuring objects and calculating relations
that they used to build monuments like the
pyramids.
The Greeks called this geometry, which means earth-
measurement.
About
300BC,
a Greek called
Euclid,
who
lived in Egypt, developed
proofs
of the geometric rules that the
Egyptians had devised.
Euclid's proofs started from
axioms
and
reasoned logically from them to conclusions.
This has been seen by some philosophers as a model for what science (or
part of Science) should be.
Hobbes
argued for
a Social Science based on Euclidian methods.
Poincare
used Euclidian and other
geometries to argue that science is based on imagination.
The 3,4,5 rule
Take three
straight lines
Make one 3 units long,
make another 4 units long,
make the other 5 units long.
Join them together to make a triangle.
The angle opposite the
longest line
will
always be a
right angle.
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The Egyptians,
who discovered
the 3,4,5
rule, used it to build
pyramids.
The 3,4,5 rule is connected to these numbers:
5 x 5 = 25 (the square of 5)
4 x 4 = 16 (the square of 4)
3 x 3 = 9 (the square of 3)
16 + 9 = 25 (4 squared, plus 3 squared, equals 5 squared)
It is a specific example of a general rule that:
In a right angled triangle, the square of the line opposite the right angle
is equal to the squares of the other two lines added together.
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This formula has been called "Pythagoras's Theorem". I do not know if Pythagoras
discovered it, but he and his followers probably saw religious significance
in it.
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Maths index
Pictures, shape, design
Figure Home Page
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Geometry
Measuring the earth
Euclid's definitions
Squares, Cubes and Roots
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