Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

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

 Messages: [ Previous | Next ]
 kirby urner Posts: 2,476 Registered: 11/29/05
Re: When math makes sense - w/ cooking, consruction
Posted: May 28, 2013 7:54 PM

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

w = get_width(h)
return w/(2*pi)

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

for h in [ 0.1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.4, 11.49, 92 ]:
w = get_width(h)

Running the above:

Paper surface of 8.5 x 11 = 93.5 square inches
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
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 Jerry P. Becker
5/4/13 Wayne Bishop
5/7/13 kirby urner
5/8/13 Greg Goodknight
5/9/13 kirby urner
5/9/13 Greg Goodknight
5/9/13 kirby urner
5/9/13 Greg Goodknight
5/9/13 kirby urner
5/9/13 Greg Goodknight
5/10/13 kirby urner
5/10/13 Greg Goodknight
5/11/13 kirby urner
5/9/13 kirby urner
5/12/13 Wayne Bishop
5/18/13 kirby urner
5/18/13 Anna Roys
5/19/13 kirby urner
5/20/13 Robert Hansen
5/22/13 kirby urner
5/24/13 Richard Strausz
5/24/13 kirby urner
5/24/13 Wayne Bishop
5/25/13 Robert Hansen
5/25/13 Anna Roys
5/27/13 Robert Hansen
5/27/13 kirby urner
5/25/13 kirby urner
5/27/13 Richard Strausz
5/27/13 Robert Hansen
5/27/13 Louis Talman
5/27/13 Robert Hansen
5/27/13 Wayne Bishop
5/28/13 Louis Talman
5/28/13 Louis Talman
5/29/13 Wayne Bishop
5/30/13 Robert Hansen
5/31/13 Wayne Bishop
5/30/13 Louis Talman
5/29/13 Robert Hansen
5/30/13 Louis Talman
5/30/13 Robert Hansen
5/30/13 kirby urner
5/31/13 Robert Hansen
5/31/13 kirby urner
5/31/13 Anna Roys
6/2/13 Robert Hansen
6/3/13 kirby urner
6/3/13 Robert Hansen
6/3/13 kirby urner
6/3/13 Robert Hansen
6/3/13 kirby urner
6/3/13 Robert Hansen
6/3/13 kirby urner
6/4/13 Robert Hansen
6/4/13 kirby urner
6/4/13 Robert Hansen
6/3/13 Robert Hansen
5/27/13 Richard Strausz
5/27/13 Robert Hansen
5/27/13 Richard Strausz
5/28/13 kirby urner
5/29/13 Wayne Bishop
5/29/13 kirby urner
5/29/13 Richard Strausz
5/29/13 Robert Hansen
5/30/13 Wayne Bishop
6/8/13 GS Chandy
6/9/13 GS Chandy
6/9/13 Robert Hansen
6/10/13 GS Chandy
6/10/13 Robert Hansen
6/10/13 kirby urner
6/10/13 Robert Hansen
6/10/13 kirby urner
6/10/13 Robert Hansen
6/10/13 kirby urner
6/10/13 Robert Hansen
6/11/13 kirby urner
6/10/13 Robert Hansen
6/10/13 Louis Talman
6/12/13 GS Chandy
6/12/13 Robert Hansen
6/13/13 GS Chandy
6/14/13 GS Chandy