Math Is Fun Forum

msw

Member

Registered: 2008-04-04

Posts: 2

Geometry: symmetry

How would you describe the symmetry arrangement of the stars on the American Flag?
vertical, horizontal, point, diagonal lines of symmetry?

What regular playing cards have point symmetry and line symmetry?

Thanks!

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Geometry: symmetry

If you use a mirror and put a flat edge on the flag, and try to make both the real and mirror parts line up.
You will probably find that a vertical line works best so the stars don't go up-side-down.

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igloo myrtilles fourmis

kgore

Member

Registered: 2008-04-04

Posts: 1

Re: Geometry: symmetry

A cola machine is set to dispense an average of 2.02 liters into a bottle labeled 2 liters. Actual quantities dispensed vary and the amounts are normally distributed with a standard deviation of 0.015 liter.
What is the probability a bottle will contain between 2.oo to 2.03 liters?
Discuss how you arrive at the probability below the mean?
How about the probability above the mean?
Discuss the probability that a bottle contains exactly 2.02 liters.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Geometry: symmetry

Well I'm a stickler for misuses of the normal function, even though I'm not good at it.
The normal function in your case must be truncated on the left side when a volume of
zero happens rarely because you can't have negative volumes.
So the this normal curve is not really a normal curve, but maybe just an estimate anyway.
I might be wrong, but it is a bell curve that goes forever in both directions.

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Geometry: symmetry

But anyway, -4/3=Z <  (your range is between)  < +2/3=Z
Look -1.3333 and +0.66667 up in a chart.
Sometimes the charts go from the middle, they are the best for this.
If not, subtract 50% or divide by 2 or multiply by 2 as needed
for the diagram to work out.

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igloo myrtilles fourmis

msw

Member

Registered: 2008-04-04

Posts: 2

Re: Geometry: symmetry

What would the radius be of a sphere such that the surface area(in sq unites) is equal to the volume (in cubic units)?

msw

Member

Registered: 2008-04-04

Posts: 2

Re: Geometry: symmetry

What would the greatest dimensions be of a rectangular prism given the surfacejavascript:insert_text('', '');
area = 64 sq inches?javascript:insert_text('', '');

Last edited by msw (2008-04-28 16:37:31)

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Geometry: symmetry

sphere radius is 3 units.
Why?  Because
(4/3)pi r r r = 4 pi r r
divide by 4 on both sides.
(1/3) pi r r r = pi r r
divide by pi r r on both sides
(1/3) r = 1
mult by 3 on both sides
r = 3
That's the answer.

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igloo myrtilles fourmis

msw

Member

Registered: 2008-04-04

Posts: 2

Re: Geometry: symmetry

Thanks for your help.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Geometry: symmetry

rectangular prism:
32 = xy + xz + yz
There are many, many answers to this!!
I'll look for a 3-D grapher...

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Geometry: symmetry

I found an implicit grapher in 3-D for free.
I graphed this:
0.1  > abs(x*y + x*z + y*z - 32) from ranges 0 to 8 for x,y,z
and it looks kind of bowl-like at this close range.
and
5 > abs(x*y + x*z + y*z -32)  from ranges 0 to 88 for x,y,and z
It looks like the inside of a cool steering wheel with 3 stems that
go out to the steering wheel not part of the graph.

Software I found is:
Imp View 3D
Written and Created by Lewey Geselowitz

Because it is for implicit equations, you must specify a
range like I did with the absolute value and the less than sign
inorder to get an approximate idea what the function
looks like, supposing it is somewhat continuous, then you
can rely on the image to some degree.

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igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Geometry: symmetry

So you see if there was just one answer to the prism, then
the graph would just be that one little point where (x,y,z)
are constant numbers like (2,3,26/5), which is just
one of many, many answers.
Just try guessing the 1st two numbers, and then try to
get the last number, that's what I did above for
x=2
y = 3
z = 26/5   (the numerator is 26 is (32 - 3*2))
the denominator is 2 + 3

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igloo myrtilles fourmis