3. The Pythagorean Order
O Students at the Pythagorean School had
to live by strict rules since they all strove
to create pure minds and bodies.
O They all thought that the mind could be
purified through studying Geometry,
mathematics, music, and astronomy.
4. The Pythagorean Order
O Women were allowed to join the Order, but
they were kept separated from the rest of the
Order.
5. Pythagorean Theorem
What does the formula mean?
O a² + b² = c² means that in a right the
sum of the squares of the lengths of two
legs equals the square of the length of the
hypotenuse.
c
a
For a more in-depth look at how this
formula was derived, check out this
site:
http://forum.swartmore.edu/~sarah/ha
milton/ham.rttriangles.tml b
6. There are Many Types of Triangles:
Can you name them?
Click on the names for the answers.
Scalene
Isosceles
Equilateral
Acute
Obtuse
Equiangular Triangle
Right Triangle
7. Important Contributions
O Pythagoras found mathematical relationships as the
essence of all things.
O He believed that the earth was spherical and that the sun,
moon, and planets have movements of their own. This
contributed to the discovery that the earth revolved around
the sun.
O He’s credited with developing the Pythagorean Theorem
which is a formula that is used to determine the lengths of
the sides of right triangles.
O His discoveries laid the foundation for all subsequent
developments in Geometry.
8. WHAT IS A RIGT TRIANGLE ?
O The Pythagorean Theorem
applies only to right triangles.
O A right triangle is a triangle that
has a 90 degree right angle. It
has two legs and a hypotenuse.
a
c O The hypotenuse is the side
opposite the right angle and is
b
always the longest.
O The variables a + b are used for
the legs and c is the variable for
the hypotenuse.
9. Let’s See How it Works!
Find the Hypotenuse
Question: If a = 3 and b = 4, then what does c equal?
a² + b² = c²
(3)2 + (4)2 = c²
(3x3) + (4x4) = c²
9 + 16 = c²
25 = c2 a
25 = c²
5 = c
b
10. How to Find a Leg
If a = 5 and c = 13, then what does b equal?
O a² + b² = c²
52 + b² = 13²
(5x5) + b² = (13x13) c
25 + b² = 169 a
25 + b² - 25 = 169 - 25
b² = 144
b² = 144 b
b = 12
11. READ THE NOTES IN THE LINK BELOW BEFORE
ATTEMPTING THE ASSESMENTS
http://www.math.com/school/subject3/lessons/S3U4L
1GL.html
FINDING A SQUARE ROOT WITHOUT A
CALCULATOR
http://www.math.com/school/subject1/lessons/S1U1L9
DP.html
12. ONLINE ASSESMENT
Click o the link below and complete the tasks before viewing the
memorandum
http://www.math-aids.com/Pythagorean_Theorem/Pythagoras.html
FOLLOW THE LINK BELOW TO HAVE PYTHAGOREAN FUNY GAMES
http://www.math-play.com/Pythagorean-Theorem-Game.html
FOLLOW THE LINK BELOW TO CALCULATE ANY SQUARE ROOT
http://www.math.com/students/calculators/source/square-root.htm
13. PHYTHAGOREAN FACTS AND FILES
Many proofs of the Pythagorean theorem:
http://www.cut-the-knot.com/pythagoras/
And again: http://www.mcn.net/~jimloy/pythag.html
History and several proofs:
http://jwilson.coe.uga.edu/emt669/Student.Folders/Mo
rris.Stephanie/EMT.669/Essay.1/Pythagorean.html
Dr. Math's Pythagorean theorem page:
http://forum.swarthmore.edu/dr.math/faq/faq.pythagore
an.html
Uses of the Pythagorean theorem:
http://www.geocities.com/primes135/uses.html
14. REFERENCES
K von Fritz, Biography in Dictionary of Scientific Biography (New York 1970-1990).
http://www.encyclopedia.com/doc/1G2-2830903544.html
ASSESED 12 APRIL 2012
Biography in Encyclopaedia Britannica.
http://www.britannica.com/eb/article-9062073/Pythagoras
ACCESED 30 APRIL 2012
Books:
R S Brumbaugh, The philosophers of Greece (Albany, N.Y., 1981).
Buckle Down on Virginia Mathematics, SOL 8, 2nd Edition by Buckle
Down Publishing Co.
Lesson 7, page 67-70
15. BEST WIHSHES FROM
PROFESSOR
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