2. P YTHAGOREAN HISTORY
The Pythagorean theorem takes its name from the
ancient Greek mathematician Pythagoras (569-500
B.C.), who was perhaps the first to offer a proof of the
theorem.
The Pythagorean theorem states that the sum of the
squares of the lengths of the two other sides of any
right triangle will equal the square of the length of the
hypotenuse, or in mathematical terms for the triangle
shown at the bottom, a2 + b2 = c2. Integers that satisfy
the conditions a2 + b2 = c2 are called ‘Pythagorean
triples’
3. P YTHAGOREAN H ISTORY:
C ONTINUED
Ancient Indian mathematicians also knew the
Pythagorean theorem, and the Sulbasutras (of
which the earliest date from ca. 800-600 B.C.)
discuss it in the context of strict requirements for
the orientation, shape, and area of altars for
religious purposes.
It has also been suggested that the ancient
Mayas used variations of Pythagorean triples in
their Long Count calendar.
4.
5. E XAMPLE : PART 1
The simplest triangle with sides of integer length
is the 3-4-5 triangle. The numbers 3,4 and 5
satisfy the rule 3²+4²=5²
This is worked out like this:
3²=9, 4²=16 and 5²=25 so
9+16=25
The set of numbers (3,4,5) is called a
Pythagorean Triple because since it obeys the
a²+b²=c² rule.
6. E XAMPLE : PART 2
There are other triangles which do not obey the
Pythagorean Triple rule, for instance the (3-7-9)
triangle does not obey the rule because:
3²=9, 7²=49 and 9²=81, but
9+49=58, there is a difference of 23
The set of numbers (3-7-9) is not classified as a
Pythagorean triple. There are many triangles just
like the one shown, they do not satisfy the
Pythagorean Triple Rule.
7.
8. Q UESTIONS
1) Show that {3, 4, 5} is a Pythagorean Triple?
2) Is {6, 8, 10} a Pythagorean Triple? Explain
why?
3) Is {9, 12, 15} a Pythagorean Triple? Explain
why?
4) Find x if {18, 24, x} is a Pythagorean Triple?
9. U SES IN B UILDINGS
The picture to the bottom shows excavating putting in
flooring deals with squares and triangles using the
Pythagorean Theorem. Some builders use this
formula, because they can find the missing sides. So
as you can see, the Pythagorean Theorem is used in
building houses and buildings.
10.
11. U SES IN E VERYDAY L IFE
Find the answers about the baseball diamond
e.g. How far the catcher has to throw the ball
to get from home plate to second base.
What type of ladder you will need to get to your
roof
You could use it to determine the distance
between two places.
12. U SES IN A RT
Pythagoras greatly admired the arts and
even thought of himself as an artist.
Artists use the triangle as pieces in a mosaic
or the shape in drawings.
Some artists use the triangle as a drawing
tool.
Pythagoras had created the triangle and the
ideas on how to use it.
