Jeff Goodman goodmanjmappstateedu Why does math matter Solve for X X 2 81126 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 ID: 391660
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Slide1
From the Concrete to the Abstract and Back
Jeff Goodman
goodmanjm@appstate.eduSlide2
Why does math matter?Slide3
Solve for X:
X
2
+81=126Slide4Slide5Slide6Slide7Slide8Slide9Slide10Slide11Slide12Slide13Slide14Slide15Slide16Slide17
What information is necessary to define these shapes?Slide18
What
’
s the best way to define these curves?Slide19Slide20
What math is behind a set of stairs?Slide21
For stairs to be comfortable, they should be proportioned by the formula:
2 x (riser height) + (tread length) = between 24 and 26 inchesSlide22
RISERSSlide23
With 10 more rises on the straightaway, I would have 13 rises total.
RISERSSlide24
102.75/ 13 = 7.9
RISERSSlide25
I had 8 feet of floor space to put in 10 stairs on the straight run
TREADSSlide26
So the tread for each stair would be:
8 feet
96 inches
/ 10 =
9.6 inches per stair
TREADSSlide27
How did I do with the formula for comfort?
2 x (riser height) + (tread length) = between 24 and 26 inches
Risers = 7.9 inches
Treads = 9.6 inches
(2 x 7.9) + 9.6 = 25.4Slide28Slide29Slide30Slide31Slide32Slide33Slide34
120/70Slide35Slide36Slide37
Where does math come from?Slide38Slide39
1
2
3
4
5
6
7
8
10
9Slide40Slide41
1 2 3 4 5 6 7 8 9
Λ
Ω
Twenty two: 1
Λ
One twelve
Plus ten
ten
eleven
Base 12Slide42Slide43
Jeff is: 110001 years old
Base 2Slide44
What’s special about 60?Slide45
30
30Slide46Slide47
2
0
2
0
2
0Slide48Slide49
15
15
15
15Slide50Slide51
12
12
12
12
12Slide52Slide53
10
10
10
10
10
10Slide54Slide55
36°12′41″N 81°40′7″W
degrees
minutes
secondsSlide56
What are the benefits of returning to concrete relationships as we solve problems?Slide57
GED 2014Slide58Slide59Slide60
What are the benefits of making math abstract?Slide61Slide62
What are the pitfalls of making math abstract?
Slide63
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:
π
dh/144*p/9Slide64
Why return to the real world to check our answers?Slide65Slide66Slide67
The Bowling Ball Pendulum Wave: a real life exampleSlide68Slide69Slide70Slide71Slide72
Real World
Physical Representation
Abstraction
Increasingly abstract
Test out on real world