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PHYTHAGOREAN THEOREM AND ITS ORIGIONS

HISTORY OF PYTHAGORASBirthplace

of Pythagoras

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.

The Pythagorean Order

OWomen were allowed to join the Order, but they were kept separated from the rest of the Order.

Pythagorean TheoremWhat 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.

a

b

c

For a more in-depth look at how this formula was derived, check out this site:

http://forum.swartmore.edu/~sarah/hamilton/ham.rttriangles.tml

There are Many Types of Triangles:Can you name them?

Click on the names for the answers.

Scalene IsoscelesEquilateralAcuteObtuseEquiangular

TriangleRight Triangle

Important ContributionsO 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.

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.

O The hypotenuse is the side opposite the right angle and is always the longest.

O The variables a + b are used for the legs and c is the variable for the hypotenuse.

a

b

c

Let’s See How it Works!Find the Hypotenuse

a² + b² = c² (3)2 + (4)2 = c²(3x3) + (4x4) = c²9 + 16 = c²

25 = c2

25 = c² 5 = c

a

b

Question: If a = 3 and b = 4, then what does c equal?

How to Find a Leg

Oa² + b² = c² 52 + b² = 13²(5x5) + b² = (13x13)25 + b² = 16925 + b² - 25 = 169 - 25

b² = 144 b² = 144

b = 12

a

b

c

If a = 5 and c = 13, then what does b equal?

NOTESOpen the link below and follow instructions then do an online activity

http://www.math-aids.com/Pythagorean_Theorem/Definition.html

READ THE NOTES IN THE LINK BELOW BEFORE ATTEMPTING THE ASSESMENTShttp://www.math.com/school/subject3/lessons/S3U4L1GL.html

FINDING A SQUARE ROOT WITHOUT A CALCULATOR

http://www.math.com/school/subject1/lessons/S1U1L9DP.html

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

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/Morris.Stephanie/EMT.669/Essay.1/Pythagorean.html

Dr. Math's Pythagorean theorem page: http://forum.swarthmore.edu/dr.math/faq/faq.pythagorean.html

Uses of the Pythagorean theorem: http://www.geocities.com/primes135/uses.html

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

Good Luck Wiz Kids!

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PMANGENA 12@GMAIL .COM

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