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Pythagorean Theorem
By: Gibran Carter
About Pythagoras
Pythagoras is often referred to as the first pure mathematician. He was
born on the island of Samos, Greece in 569 BC. Various writings place
his death between 500 BC and 475 BC in Metapontum, Lucania, Italy.
Pythagoras was well educated, and he played the lyre throughout his
lifetime, knew poetry and recited Homer. He was interested in
mathematics, philosophy, astronomy and music, and was greatly
influenced by Pherekydes (philosophy), Thales (mathematics and
astronomy) and Anaximander (philosophy, geometry).
Pythagoras studied odd and even numbers, triangular numbers, and
perfect numbers. Pythagoreans contributed to our understanding of
angles, triangles, areas, proportion, polygons, and polyhedra.
Pythagoras also related music to mathematics. He had long played the
seven string lyre, and learned how harmonious the vibrating strings
sounded when the lengths of the strings were proportional to whole
numbers, such as 2:1, 3:2, 4:3. Pythagoreans also realized that this
knowledge could be applied to other musical instruments.
The Formula
In any right-angled triangle, the area of the square whose side is the
hypotenuse (the side opposite the right angle) is equal to the sum of
the areas of the squares whose sides are the two legs (the two sides
that meet at a right angle).
How is the Pythagorean Theorem
applied to every day life?
Architecture and Construction
Navigation
Earthquake Location
Crime Scene Investigation
Arrow & Missile Trajectory
Objectives
Students will learn:
How to solve an equation using
the Pythagorean Theorem
How to recognize a right Triangle
Able to locate where the
hypotenuse is
Fact:
 The longest side of the triangle
is called the "hypotenuse"
If we know the lengths of two sides of a
right angled triangle, we can find the length
of the third side. (But remember it only
works on right angled triangles!)
What is a right triangle?
A right triangle or right-angled
triangle is a triangle in which
one angle is a right angle (that
is, a 90-degree angle). The
relation between the sides and
angles of a right triangle is the
basis for trigonometry.
Here is the equation:
How do I use the equation to solve the
problem?
First, you will write the equation down
The steps of the Theorem:
a2 + b 2 = c 2
52 + 122 = c2
25 + 144 = c2
169 = c2
c2 = 169
c = √169
c = 13