Pythagoras

This powerpoint is about Pythagoras, his theorem, and shapes

1. Geometry and Geometry and
MeasurementMeasurement
Brad Fewins
Stephen Hummel

2. Table of Contents:Table of Contents:
Pythagorean TheoremPythagorean Theorem
•Pythagoras of SamosPythagoras of Samos
•HistoryHistory
•More on HistoryMore on History
•Pythagoras QuotesPythagoras Quotes
•References to the Pythagorean TheoremReferences to the Pythagorean Theorem
•More ReferencesMore References
•Proving the TheoremProving the Theorem
•Real-World ApplicationReal-World Application
•Works CitedWorks Cited

3. Table of Contents: ShapesTable of Contents: Shapes

Circle Circle

TriangleTriangle

SquareSquare

RectangleRectangle

RhombusRhombus

Additional HelpAdditional Help

Works CitedWorks Cited

4. Pythagoras of SamosPythagoras of Samos
•Pythagoras was an extremely important
mathematician in history.
•He is called the first pure
mathematician by many.
•Unfortunately, we know relatively little
about his mathematical achievements.
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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.
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6. More on history
•Pythagoras, whose dates are commonly
given as 569–475 BC, used algebraic
methods to construct Pythagorean triples.
There is a legend that Pythagoras sacrificed
100 oxen in light of the discovery.
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7. Pythagoras Quotes
•Number is the ruler of forms and ideas, and
the cause of gods and demons.
•Every man has been made by God in order to
acquire knowledge and contemplate.
•Geometry is knowledge of the eternally
existent.
•Number is the within of all things.
•There is geometry in the humming of the
strings.
•Time is the soul of this world.
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8. References to the Pythagorean
Theorem
•~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, "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!"
•~In an episode of the Simpson's, Homer quotes the
scarecrow’s version of the theorem A man nearby then
yells out, "That's a right triangle, you idiot!" (although that
still doesn’t completely correct the scarecrows version)
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9. More References
•~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.
•~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.
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10. Proving the TheoremProving the Theorem
•This website includes an interactive
java applet that allows the audience to
follow along well enough to understand
the geometry involved.
•http://www.sunsite.ubc.ca/LivingMathematics/V001N01/UBCExamples/Pythagoras/pythagoras.htmlhttp://www.sunsite.ubc.ca/LivingMathematics/V001N01/UBCExamples/Pythagoras/pythagoras.html
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11. Return to Pythagoras Menu

12. The answer to this real world
application
•a=90 Since the distance
•b=90 between home plate
•c^2=a^2+b^2 and second base is
•c^2=90^2+90^2 the same as the
•c^2=8100+8100 distance between
•c^2=16200 first base and third
•c= base, the answer for
•c=127.279 both distances will be
Back to the problem the same.
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13. CircleCircle
Area of a Circle:Area of a Circle:

A=A=∏(3.14)·r²∏(3.14)·r²

Or Or ∏∙r∙r∏∙r∙r

Example:Example:

R= 3 inches, what is R= 3 inches, what is
the area?the area?

∏∙ ∏∙3 inches·3 inches = 28.26in²3 inches·3 inches = 28.26in²
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14. TriangleTriangle
Area=Area=
½· base · height½· base · height
Base=12cmBase=12cm
Height=9cmHeight=9cm

½·12·9=½·12·9=

Click image to Click image to
reveal answer!reveal answer!

15. Answer:Answer:
A=A=½·108 in²=½·108 in²=
A=54 inches²A=54 inches²
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16. SquareSquare

Area= width Area= width · height· height

X= 6 meters, what isX= 6 meters, what is
the area?the area?

6m·6m=6m·6m=

36m²36m²
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17. RectangleRectangle

Area=Area= Width Width · Height· Height

If s=4, what is the Area?If s=4, what is the Area?

Click image for answerClick image for answer

18. Solution:Solution:
If s= 4cmIf s= 4cm

Area= 9cmArea= 9cm · 4cm · 4cm

Answer= Answer= 36cm²36cm²
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19. RhombusRhombus
Area for base times Area for base times
height method:height method:
Click image for solution!Click image for solution!
Area=Area=
base base · altitude or · altitude or
heightheight

Example:Example:

If base= 129cmIf base= 129cm

Height= 34cmHeight= 34cm

Area= ?Area= ?

20. Answer: RhombusAnswer: Rhombus

Area= 129cm Area= 129cm · 34cm=· 34cm=

4386 cm²4386 cm²
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21. Additional Help
Area of a Circle
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22. Additional Help
Area of a Rectangle
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23. Works cited
•http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Pythagoras.html
•http://en.wikipedia.org/wiki/Pythagorean_theorem
•http://www.geom.uiuc.edu/~demo5337/Group3/hist.html
•http://www.sunsite.ubc.ca/LivingMathematics/V001N01/UBCExamples/Pythagoras/pythagoras.html
•http://www.youtube.com/watch?v=1ZReTq9V2RI
•http://www.youtube.com/watch?v=ECJfSyg_Obo
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