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This powerpoint is about Pythagoras, his theorem, and shapes

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  1. 1. Geometry and Measurement Brad Fewins Stephen Hummel
  2. 2. Table of Contents: Pythagorean Theorem <ul><li>Pythagoras of Samos </li></ul><ul><li>History </li></ul><ul><li>More on History </li></ul><ul><li>Pythagoras Quotes </li></ul><ul><li>References to the Pythagorean Theorem </li></ul><ul><li>More References </li></ul><ul><li>Proving the Theorem </li></ul><ul><li>Real-World Application </li></ul><ul><li>Works Cited </li></ul>
  3. 3. Table of Contents: Shapes <ul><li>Circle </li></ul><ul><li>Triangle </li></ul><ul><li>Square </li></ul><ul><li>Rectangle </li></ul><ul><li>Rhombus </li></ul><ul><li>Additional Help </li></ul><ul><li>Works Cited </li></ul>
  4. 4. Pythagoras of Samos <ul><li>Pythagoras was an extremely important mathematician in history. </li></ul><ul><li>He is called the first pure mathematician by many. </li></ul><ul><li>Unfortunately, we know relatively little about his mathematical achievements. </li></ul>Return to Pythagoras Menu
  5. 5. History There is a lot of debate whether the theorem was discovered once or many times. Many believe that the theorem was known to the Babylonians 1000 years previous to Pythagoras but he may have been the first to prove it. Return to Pythagoras Menu
  6. 6. More on history <ul><li>Pythagoras , whose dates are commonly given as 569–475 BC, used algebraic methods to construct Pythagorean triples. </li></ul>There is a legend that Pythagoras sacrificed 100 oxen in light of the discovery. Return to Pythagoras Menu
  7. 7. Pythagoras Quotes <ul><li>Number is the ruler of forms and ideas, and the cause of gods and demons. </li></ul><ul><li>Every man has been made by God in order to acquire knowledge and contemplate. </li></ul><ul><li>Geometry is knowledge of the eternally existent. </li></ul><ul><li>Number is the within of all things. </li></ul><ul><li>There is geometry in the humming of the strings. </li></ul><ul><li>Time is the soul of this world. </li></ul>Return to Pythagoras Menu
  8. 8. References to the Pythagorean Theorem <ul><li>~In the Wizard of Oz when the scarecrow gets his diploma from the wizard he immediately shows off his knowledge by exclaiming an incorrect version of the formula, &quot;The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side. Oh, joy, oh, rapture. I've got a brain!&quot; </li></ul><ul><li>~In an episode of the Simpson's, Homer quotes the scarecrow’s version of the theorem A man nearby then yells out, &quot;That's a right triangle, you idiot!&quot; (although that still doesn’t completely correct the scarecrows version) </li></ul>Return to Pythagoras Menu
  9. 9. More References <ul><li>~The speech software on the MacBook also references the previous incorrect statement of the theorem. It is a sample speech, Ralph is the voice setting. </li></ul><ul><li>~Also, Uganda released a coin with the shape of a right triangle inscribed on it. The coin has a picture of Pythagoras and the Pythagorean theorem on it. </li></ul>Return to Pythagoras Menu
  10. 10. Proving the Theorem <ul><li>This website includes an interactive java applet that allows the audience to follow along well enough to understand the geometry involved. </li></ul><ul><li> </li></ul>Return to Pythagoras Menu
  11. 11. Return to Pythagoras Menu
  12. 12. The answer to this real world application <ul><li>a=90 Since the distance </li></ul><ul><li>b=90 between home plate </li></ul><ul><li>c^2=a^2+b^2 and second base is </li></ul><ul><li>c^2=90^2+90^2 the same as the </li></ul><ul><li>c^2=8100+8100 distance between </li></ul><ul><li>c^2=16200 first base and third </li></ul><ul><li>c= base, the answer for </li></ul><ul><li>c=127.279 both distances will be </li></ul><ul><li>Back to the problem the same. </li></ul>Click Image to Return to Pythagoras Menu
  13. 13. Circle <ul><li>Area of a Circle: </li></ul><ul><ul><li>A= ∏(3.14)·r² </li></ul></ul><ul><ul><ul><li>Or ∏∙r∙r </li></ul></ul></ul><ul><li>Example: </li></ul><ul><ul><li>R= 3 inches, what is </li></ul></ul><ul><ul><li>the area? </li></ul></ul><ul><ul><ul><li>∏∙ 3 inches·3 inches = 28.26in² </li></ul></ul></ul><ul><ul><ul><li>Return to Shapes Menu </li></ul></ul></ul>
  14. 14. Triangle <ul><li>Area= </li></ul><ul><ul><li>½· base · height </li></ul></ul><ul><li>Base=12cm </li></ul><ul><li>Height=9cm </li></ul><ul><li>½·12·9= </li></ul><ul><ul><li>Click image to reveal answer! </li></ul></ul>
  15. 15. Answer: A= ½·108 in²= A=54 inches² Return to Shapes Menu
  16. 16. Square <ul><li>Area= width · height </li></ul><ul><li>X= 6 meters, what is </li></ul><ul><li>the area? </li></ul><ul><ul><li>6m·6m= </li></ul></ul><ul><ul><ul><li>36m² </li></ul></ul></ul><ul><ul><ul><li>Return to Shapes Menu </li></ul></ul></ul>
  17. 17. Rectangle <ul><li>Area= Width · Height </li></ul><ul><li>If s=4, what is the Area? </li></ul><ul><li>Click image for answer </li></ul>
  18. 18. Solution: <ul><li>If s= 4cm </li></ul><ul><ul><li>Area= 9cm · 4cm </li></ul></ul><ul><li>Answer= 36cm² </li></ul><ul><li>Return to Shapes Menu </li></ul>
  19. 19. Rhombus <ul><li>Area for base times height method: </li></ul><ul><li>Click image for solution! </li></ul><ul><li>Area= </li></ul><ul><li>base · altitude or height </li></ul><ul><li>Example: </li></ul><ul><ul><li>If base= 129cm </li></ul></ul><ul><ul><li>Height= 34cm </li></ul></ul><ul><ul><li>Area= ? </li></ul></ul>
  20. 20. Answer: Rhombus <ul><li>Area= 129cm · 34cm= </li></ul><ul><li>4386 cm² </li></ul><ul><li>Return to Shapes Menu </li></ul><ul><li>Return to Pythagoras Menu </li></ul>
  21. 21. Additional Help <ul><li>Area of a Circle </li></ul><ul><li>Return to Shapes Menu </li></ul>
  22. 22. Additional Help <ul><li>Area of a Rectangle </li></ul><ul><li>Return to Shapes Menu </li></ul>
  23. 23. Works cited <ul><li> </li></ul><ul><li>http:// </li></ul><ul><li> </li></ul><ul><li> </li></ul><ul><li>http:// =1ZReTq9V2RI </li></ul><ul><li>http:// = ECJfSyg_Obo </li></ul>Return to Pythagoras Menu Return to Shapes Menu