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Topic: When math makes sense - w/ cooking, consruction
Replies: 84   Last Post: Jun 14, 2013 12:33 AM

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kirby urner

Posts: 1,673
Registered: 11/29/05
Re: When math makes sense - w/ cooking, consruction
Posted: May 28, 2013 7:54 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Taking a more algebraic approach, using the tools I'd
expect in a STEM class for the age of the student in the
video, I find that the best strategy for maximizing
volume is to maximize the radius and minimize the height.

If you have a fixed surface area equal to 8.5 x 11 inches,
or 93.5 square inches, then cut very narrow strips and
splice them together to make as giant a circle as you can.

Looking at the formula, this makes sense because w and
h are inversely proportional and h * w always multiplies
to the same answer. However, if we make r a function of
width and V = pi * radius * radius * height
then clearly investing in radius is best, as it's a 2nd
power payout, whereas investing in height is less bang
for the buck.

A height of 92 inches means a tube with a radius of 0.16
inches, a circumference of just a tiny bit over an inch.

The volume will be only 7.56 cubic inches whereas if you
have a height of 0.1 inches your width will be 935 inches
(almost 78 feet around) and your volume will be a
whopping 6956.9 cubic inches, which is huge.

A vast circular shallow lake is the way to go,
versus a tall thin tubular straw. The latter maximizes
surface to volume, whereas the former minimizes it.

Kirby

You'll need to view the plaintext version of this post
in the archives (button upper right) if you want this
code to be indented properly; Python has significant
whitespace meaning indentation is used when parsing.
The table also looks better when the tabs (\t) are not
ignored (HTML suppresses whitespace by design).

Note that Width is defined as the circumference of the
cylinder, as if unrolled to make a rectangular sheet.


from math import pi

def cylvol(height, radius): return pi * radius**2 * height

def get_width(height):
return (8.5)*(11)/height

def get_radius(h):
w = get_width(h)
return w/(2*pi)

print("Paper surface of 8.5 x 11 =", 8.5 * 11, "square inches")

print("Height:","Width:","Radius:","Surface:","Vol:", sep="\t")
for h in [ 0.1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.4, 11.49, 92 ]:
r = get_radius(h)
w = get_width(h)
columns = "{height:>6.2f}\t{width:>6.2f}\t{radius:>6.2f}\t{surface:6.2f}\t{volume:>8.2f}"
print(columns.format(height=h,width=w,radius=r,surface=h*w,volume=cylvol(h,r)))


Running the above:

Paper surface of 8.5 x 11 = 93.5 square inches
Height: Width: Radius: Surface: Vol:
0.10 935.00 148.81 93.50 6956.86
1.00 93.50 14.88 93.50 695.69
2.00 46.75 7.44 93.50 347.84
3.00 31.17 4.96 93.50 231.90
4.00 23.38 3.72 93.50 173.92
5.00 18.70 2.98 93.50 139.14
6.00 15.58 2.48 93.50 115.95
7.00 13.36 2.13 93.50 99.38
8.00 11.69 1.86 93.50 86.96
9.00 10.39 1.65 93.50 77.30
10.00 9.35 1.49 93.50 69.57
11.40 8.20 1.31 93.50 61.03
11.49 8.14 1.30 93.50 60.55
92.00 1.02 0.16 93.50 7.56

PS: if you're a high school student reading this and your
STEM classes do not give you access to free software such
as Python, then consider writing to the governor of your
state and expressing displeasure at the backwardness of
your curriculum and the unwanted negative impact on your
future this deficiency may have. Demand to have an
interactive full featured programming language in your
curriculum, not just calculators. Don't take no for an
answer. The hardware is dirt cheap and the software is
gratis. Schools that can't supply such minimal equipment
are poorly funded and administered. You deserve better.
Have more self esteem.

It's not that I think governors should really be
involved, but they've insisted in recent chapters. Also
scan these remarks and see if the content looks at all
familiar (a post in this same thread):

http://mathforum.org/kb/message.jspa?messageID=9128009

If not, more warning flags. Talk to your parents. Is
distance education possible? Sometimes neighboring
states have more enlightened options, or even far away
states. Earn academic credit off shore or overseas if
need be, using your computer as a communications device.

Do not settle for what just happens to be local, if it
also happens to be inferior.


Date Subject Author
5/4/13
Read When math makes sense - w/ cooking, consruction
Jerry P. Becker
5/4/13
Read Re: When math makes sense - w/ cooking, consruction
Wayne Bishop
5/7/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
5/8/13
Read Re: When math makes sense - w/ cooking, consruction
Greg Goodknight
5/9/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
5/9/13
Read Re: When math makes sense - w/ cooking, consruction
Greg Goodknight
5/9/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
5/9/13
Read Re: When math makes sense - w/ cooking, consruction
Greg Goodknight
5/9/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
5/9/13
Read Re: When math makes sense - w/ cooking, consruction
Greg Goodknight
5/10/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
5/10/13
Read Re: When math makes sense - w/ cooking, consruction
Greg Goodknight
5/11/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
5/9/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
5/12/13
Read Re: When math makes sense - w/ cooking, consruction
Wayne Bishop
5/18/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
5/18/13
Read Re: When math makes sense - w/ cooking, consruction
Anna Roys
5/19/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
5/20/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
5/22/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
5/24/13
Read Re: When math makes sense - w/ cooking, consruction
Richard Strausz
5/24/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
5/24/13
Read Re: When math makes sense - w/ cooking, consruction
Wayne Bishop
5/25/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
5/25/13
Read Re: When math makes sense - w/ cooking, consruction
Anna Roys
5/27/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
5/27/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
5/25/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
5/27/13
Read Re: When math makes sense - w/ cooking, consruction
Richard Strausz
5/27/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
5/27/13
Read Re: When math makes sense - w/ cooking, consruction
Louis Talman
5/27/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
5/27/13
Read Re: When math makes sense - w/ cooking, consruction
Wayne Bishop
5/28/13
Read Re: When math makes sense - w/ cooking, consruction
Louis Talman
5/28/13
Read Re: When math makes sense - w/ cooking, consruction
Louis Talman
5/29/13
Read Re: When math makes sense - w/ cooking, consruction
Wayne Bishop
5/30/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
5/31/13
Read Re: When math makes sense - w/ cooking, consruction
Wayne Bishop
5/30/13
Read Re: When math makes sense - w/ cooking, consruction
Louis Talman
5/29/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
5/30/13
Read Re: When math makes sense - w/ cooking, consruction
Louis Talman
5/30/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
5/30/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
5/31/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
5/31/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
5/31/13
Read Re: When math makes sense - w/ cooking, consruction
Anna Roys
6/2/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
6/3/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
6/3/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
6/3/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
6/3/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
6/3/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
6/3/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
6/3/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
6/4/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
6/4/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
6/4/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
6/3/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
5/27/13
Read Re: When math makes sense - w/ cooking, consruction
Richard Strausz
5/27/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
5/27/13
Read Re: When math makes sense - w/ cooking, consruction
Richard Strausz
5/28/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
5/29/13
Read Re: When math makes sense - w/ cooking, consruction
Wayne Bishop
5/29/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
5/29/13
Read Re: When math makes sense - w/ cooking, consruction
Richard Strausz
5/29/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
5/30/13
Read Re: When math makes sense - w/ cooking, consruction
Wayne Bishop
6/8/13
Read Re: When math makes sense - w/ cooking, consruction
GS Chandy
6/9/13
Read Re: When math makes sense - w/ cooking, consruction
GS Chandy
6/9/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
6/10/13
Read Re: When math makes sense - w/ cooking, consruction
GS Chandy
6/10/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
6/10/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
6/10/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
6/10/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
6/10/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
6/10/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
6/10/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
6/11/13
Read Re: When math makes sense - w/ cooking, consruction
kirby urner
6/10/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
6/10/13
Read Re: When math makes sense - w/ cooking, consruction
Louis Talman
6/12/13
Read Re: When math makes sense - w/ cooking, consruction
GS Chandy
6/12/13
Read Re: When math makes sense - w/ cooking, consruction
Robert Hansen
6/13/13
Read Re: When math makes sense - w/ cooking, consruction
GS Chandy
6/14/13
Read Re: When math makes sense - w/ cooking, consruction
GS Chandy

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