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Alpo

Check my math

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I was trying to decide which had the smaller perimeter, for the same area. I had decided on a square.

 

A square mile has four one mile long sides, making a four mile perimeter.

 

But if it was a rectangle two miles long by a half mile wide, it would still be one square mile, but would take two pieces of two mile long fence and two pieces of half mile long fence, making a five mile perimeter.

 

If you took a two mile long by one mile wide rectangle, and cut it into two right triangles, you would have 1 one mile long fence (a), 1 two mile long (b) fence, and the hypotenuse (c). A² (1) + B² (4) = C² (5), so C =√5 --- 2.236. 1+2+2.236=5.236. That's longer than the rectangle.

 

Then I thought about a circle. Area of a circle = πr².

 

1 ÷ π = r² = 0.318.

√r = √0.318 =0.564.

r = 0.564, so d (2r) = 1.128

Circumference of a circle = πd

d = 1.128 x π = 3.543

 

It appears that for the same area (in my example, one square mile), the perimeter of a circle is less than anything else.

 

Does that sound right to y'all, or have I forgot something? 11th grade geometry was a long damn time ago.

 

 

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3 minutes ago, Alpo said:

I was trying to decide which had the smaller perimeter, for the same area. I had decided on a square.

 

A square mile has four one mile long sides, making a four mile perimeter.

 

But if it was a rectangle two miles long by a half mile wide, it would still be one square mile, but would take two pieces of two mile long fence and two pieces of half mile long fence, making a five mile perimeter.

 

If you took a two mile long by one mile wide rectangle, and cut it into two right triangles, you would have 1 one mile long fence (a), 1 two mile long (b) fence, and the hypotenuse (c). A² (1) + B² (4) = C² (5), so C =√5 --- 2.236. 1+2+2.236=5.236. That's longer than the rectangle.

 

Then I thought about a circle. Area of a circle = πr².

 

1 ÷ π = r² = 0.318.

√r = √0.318 =0.564.

r = 0.564, so d (2r) = 1.128

Circumference of a circle = πd

d = 1.128 x π = 3.543

 

It appears that for the same area (in my example, one square mile), the perimeter of a circle is less than anything else.

 

Does that sound right to y'all, or have I forgot something? 11th grade geometry was a long damn time ago.

 

 

Yes, Circles contain the most area of any shape relative to circumference/perimeter.

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19 minutes ago, Captain Bill Burt said:

Yes, Circles contain the most area of any shape relative to circumference/perimeter.

Which is why a puddle of oil in water is round and bubbles are spherical.

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Quote

d = 1.128 x π = 3.543

 

C = 1.128 x π = 3.543

 

Other than this typo, you are correct.

 

Consider a triangle, the area A = 1/2 base X height

 

 A rectangle area A = base X height

 

A pentagon...

 

A hexagon...

 

A septagon...

 

An octagon....

.

.

.

A circle!

 

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so what on earth prompted you go on this geometric journey ? you looking to buy land or buy fence ? seldom find a parcel of land in a rectangle or circular and the fence salesman will wonder at selling you a circular fence - but hey it was a fun walk down memory lane 

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28 minutes ago, John Kloehr said:

Other than this typo, you are correct

That wasn't a typo.

 

The circumference of a circle is pi times the diameter. πd

 

d (diameter) = 1.128

Take that 1.128 and multiply it by pi and you get an answer.

 

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14 minutes ago, watab kid said:

so what on earth prompted you go on this geometric journey ? you looking to buy land or buy fence ? seldom find a parcel of land in a rectangle or circular and the fence salesman will wonder at selling you a circular fence - but hey it was a fun walk down memory lane 

I was thinking about Louis L'Amour. One of his "these are true about me" stories (possibly in Yondering).

 

He is in Death Vallley, he is at a water hole, and there is a hubcap. He washed out the hubcap and then beat it into a different shape with a rock, so that he could use it to carry water.

 

That got me to thinking about if you had a bucket which held, for example, one gallon, and you reshaped the metal bucket, would it then hold more or less than a gallon.

 

Then I left my bucket and went to fences because area is easier to work with than volume. Two dimensions versus three.

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6 minutes ago, Alpo said:

That wasn't a typo.

 

The circumference of a circle is pi times the diameter. πd

 

d (diameter) = 1.128

Take that 1.128 and multiply it by pi and you get an answer.

 

C = 2πr =  πd = 1.128π

 

I may be drunk, but it is a typo.

 

On edit: You essentially have d = dπ

Edited by John Kloehr

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You may consider it a mistake, but a typo is when I accidentally typed something that I did not mean to type.

 

I meant to type "d", therefore it is not a typo.

 

 

You are looking at it as a formula

C (circumference) equals blah x blah x blah

 

I wrote it as what the values are

d equals 1.128, then you take that 1.128 and you multiply it by pi

Edited by Alpo

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11 minutes ago, Alpo said:

I was thinking about Louis L'Amour. One of his "these are true about me" stories (possibly in Yondering).

 

He is in Death Vallley, he is at a water hole, and there is a hubcap. He washed out the hubcap and then beat it into a different shape with a rock, so that he could use it to carry water.

 

That got me to thinking about if you had a bucket which held, for example, one gallon, and you reshaped the metal bucket, would it then hold more or less than a gallon.

 

Then I left my bucket and went to fences because area is easier to work with than volume. Two dimensions versus three.

True two dimensions is easier than three.

 

So consider a hubcap that is a slice out of a sphere. If it could be beat into a sphere, it would hold more water for the surface area of the disc (assuming the metal was not thinned as a result of working it). You are correct in your simplification to two dimensions, if the hubcap was beat into a cube, it would hold less than the maximum amount of water.

 

Now I'm thinking... Could, for a given surface area (with an open top!), a section of a sphere hold more water than a sphere? Too drunk to tackle it, probably will interfere with sleep now that I raised the question in my mind.

 

Because while a circle maximizes area and a sphere maximizes volume, an open top container needs no material on top to hold contents... So is there some bowl shape which has a greater volume than a sphere of the same surface area?

Edited by John Kloehr

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9 minutes ago, Alpo said:

You may consider it a mistake, but a typo is when I accidentally typed something that I did not mean to type.

 

I meant to type "d", therefore it is not a typo.

 

 

You are looking at it as a formula

C (circumference) equals blah x blah x blah

 

I wrote it as what the values are

d equals 1.128, then you take that 1.128 and you multiply it by pi

I am an engineer.

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I DON'T CARE!!!

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The only farmer math I learned was: The measurement of an acre is:  9 corn rows wide and 1/4 mile long.

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6 hours ago, Alpo said:

I was trying to decide which had the smaller perimeter, for the same area. I had decided on a square.

 

A square mile has four one mile long sides, making a four mile perimeter.

 

But if it was a rectangle two miles long by a half mile wide, it would still be one square mile, but would take two pieces of two mile long fence and two pieces of half mile long fence, making a five mile perimeter.

 

If you took a two mile long by one mile wide rectangle, and cut it into two right triangles, you would have 1 one mile long fence (a), 1 two mile long (b) fence, and the hypotenuse (c). A² (1) + B² (4) = C² (5), so C =√5 --- 2.236. 1+2+2.236=5.236. That's longer than the rectangle.

 

Then I thought about a circle. Area of a circle = πr².

 

1 ÷ π = r² = 0.318.

√r = √0.318 =0.564.

r = 0.564, so d (2r) = 1.128

Circumference of a circle = πd

d = 1.128 x π = 3.543

 

It appears that for the same area (in my example, one square mile), the perimeter of a circle is less than anything else.

 

Does that sound right to y'all, or have I forgot something? 11th grade geometry was a long damn time ago.

 

 

I used to teach math.  Never could get the hang of it.  Sad commentary on our school systems around the nation.

 

 

 

 

 

Edited by Forty Rod SASS 3935

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2 hours ago, Alpo said:

I was thinking about Louis L'Amour. One of his "these are true about me" stories (possibly in Yondering).

 

He is in Death Vallley, he is at a water hole, and there is a hubcap. He washed out the hubcap and then beat it into a different shape with a rock, so that he could use it to carry water.

 

That got me to thinking about if you had a bucket which held, for example, one gallon, and you reshaped the metal bucket, would it then hold more or less than a gallon.

 

Then I left my bucket and went to fences because area is easier to work with than volume. Two dimensions versus three.

 

 

i never would have gone there but it makes sense to me , i was an architect/contractor in my previous life so i jumped to conclusion on the land measurements and not without some justification given the presentation but i see where you were going , 

 

now - just to stir the pot a bit your land measurements are single plane - the hubcap after being distressed has three dimensions , you are not only talking about linear measure and the surface area now your talking volume , 

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If a sphere can hold the greatest volume for a given surface area then 1/2 a sphere will still hold the greatest volume over any other open top shape.

 

If you want it to be a closed or nearly closed container then it still needs to be in the shape of a sphere.

 

Foa sphere with a radius of 10mm

image.png.ef143488604d2e7a848367b7baead1c8.png  1/2 sphere with no top = 2094.395 Cubic cm

 

image.png.1f2246af69573d7065911f9d11760183.pngArea of 1/2 sphere with no top = 628.31853 Square cm

 

A sphere with a surface area of 628.31853 has a volume of 1480 cubic cm

 

Edited by Sedalia Dave
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A sphere maximizes volume to surface area.  In other words a round lead ball has less surface area than any other shape with the same weight

 

Which is one of the reasons why a pure lead ball can poke a hole through a deer (or enemy personnel) out of a muzzle loading firearm so efficiently.

 

Dang, SD outdrew me!  
 

Again.

 

:ph34r:

Edited by J-BAR #18287

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All in all....I think he needs to check his meds for an adjustment....Most of us, do not want to have to think that hard...It is Sunday....

 

Texas Lizard

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6 hours ago, Alpo said:

 

d = 1.128 x π = 3.543

 

While you might consider this to be correct, the notation is lazy and unacceptable.

 

d = 1.128,  d x π = 3.543

 

would be acceptable.
 

BS, MS, PhD

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Y'all are seriously making my head hurt.

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46 minutes ago, Marshal Mo Hare, SASS #45984 said:

BS, MS, PhD

Bull poop and Mule poop, piled higher and deeper?

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36 minutes ago, Alpo said:

Bull poop and Mule poop, piled higher and deeper?

If you wish but your notation is still wrong. ;)
 

oh, being in the Northeast, Moose Scat.

 

 

 

 

Edited by Marshal Mo Hare, SASS #45984
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It must have already turned too cold to venture outside in some areas. Might be a long dark winter......

 

So if cleanshot powder has a density of .65grams/cc, How many cc's to give me .45 grains? That's a more useful math question. (and I already know the answer, I think.

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17 hours ago, Noz said:

The only farmer math I learned was: The measurement of an acre is:  9 corn rows wide and 1/4 mile long.

What size are your rows?

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22 minutes ago, Chickamauga Slim said:

It must have already turned too cold to venture outside in some areas. Might be a long dark winter......

 

So if cleanshot powder has a density of .65grams/cc, How many cc's to give me .45 grains? That's a more useful math question. (and I already know the answer, I think.

4.49 ccs if you mean 45 grains. If you mean .45 grains then .0449 ccs

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1 hour ago, Chickamauga Slim said:

How many cc's to give me .45 grains?

Now that, I'm fairly certain, is a typo. :P

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3 hours ago, Alpo said:

Now that, I'm fairly certain, is a typo. :P

It is a typo,

Let's try 4.5 grains.......

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I never was good at geometry but did realize long ago, the further you go into the alphabet, the more volume to the cup.

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 What, exactly does the OP have to do whether we have Ice Cream inna freezer for desert??

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18 minutes ago, Colorado Coffinmaker said:

 What, exactly does the OP have to do whether we have Ice Cream inna freezer for desert??

I forgot, I have Hagen Daz chocolate! Thanks!

Edited by John Kloehr
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4 hours ago, sassnetguy50 said:

What size are your rows?

Whatever the planter pulled behind the mules measures.

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2 hours ago, Chickamauga Slim said:

It is a typo,

Let's try 4.5 grains.......

Then .449

Edited by Captain Bill Burt

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@Alpo  my head hurts from this....

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