WELCOME TO MATHS WITH PROFESSORPHYTHAGOREAN THEOREM AND ITS ORIGIONS
HISTORY OF PYTHAGORA S Birthplace of Pythagoras
The Pythagorean OrderO 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 OrderO Women were allowed to join the Order, but they were kept separated from the rest of the Order.
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 aFor a more in-depth look at how thisformula was derived, check out thissite:http://forum.swartmore.edu/~sarah/hamilton/ham.rttriangles.tml b
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
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.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.
Let’s See How it Works! Find the HypotenuseQuestion: 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
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
READ THE NOTES IN THE LINK BELOW BEFORE ATTEMPTING THE ASSESMENTShttp://www.math.com/school/subject3/lessons/S3U4L 1GL.html FINDING A SQUARE ROOT WITHOUT A CALCULATORhttp://www.math.com/school/subject1/lessons/S1U1L9 DP.html
ONLINE ASSESMENTClick 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/Mo rris.Stephanie/EMT.669/Essay.1/Pythagorean.html Dr. Maths 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
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
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