from the concrete to the abstract and back
DESCRIPTION
From the Concrete to the Abstract and Back. Jeff Goodman [email protected]. Why does math matter?. Solve for X: X 2 +81=126. What information is necessary to define these shapes?. What ’ s the best way to define these curves?. What math is behind a set of stairs?. - PowerPoint PPT PresentationTRANSCRIPT
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Why does math matter?
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Solve for X:X2+81=126
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What information is necessary to define these shapes?
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What’s the best way to define these curves?
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What math is behind a set of stairs?
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For stairs to be comfortable, they should be proportioned by the formula:
2 x (riser height) + (tread length) = between 24 and 26 inches
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RISERS
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With 10 more rises on the straightaway, I would have 13 rises total.
RISERS
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102.75/ 13 = 7.9
RISERS
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I had 8 feet of floor space to put in 10 stairs on the straight run
TREADS
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So the tread for each stair would be:
8 feet96 inches / 10 = 9.6 inches per stair
TREADS
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How did I do with the formula for comfort?
2 x (riser height) + (tread length) = between 24 and 26 inches
Risers = 7.9 inchesTreads = 9.6 inches
(2 x 7.9) + 9.6 = 25.4
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120/70
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Where does math come from?
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1
2
34
5
67
8
10
9
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1 2 3 4 5 6 7 8 9 Λ Ω
Twenty two: 1 Λ
One twelvePlus ten
ten eleven
Base 12
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Jeff is: 110001 years old
Base 2
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What’s special about 60?
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30 30
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20
20
20
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15 15
15 15
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12 12
12
12
12
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10 10
10
10 10
10
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36°12 41″N 81°40 7″W′ ′
degrees
minutesseconds
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What are the benefits of returning to concrete relationships as we solve problems?
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GED 2014
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What are the benefits of making math abstract?
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What are the pitfalls of making math abstract?
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Just remember, if you ever need to wrap a tree with wire and it is sold by the square yard, the amount you’ll need to pay is:
πdh/144*p/9
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Why return to the real world to check our answers?
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The Bowling Ball Pendulum Wave: a real life example
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Real WorldPhysical RepresentationAbstraction
Increasingly abstract
Test out on real world