Check my math

[Alpo 6,199]

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.

 

 

[Captain Bill Burt 2,989]

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.

[Marshal Mo Hare, SASS #45984 6,843]

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.

[John Kloehr 858]

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!

 

[watab kid 969]

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 

[John Kloehr 858]

Just don't fall for this trap:

 

[Alpo 6,199]

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.

 

[Alpo 6,199]

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.

[John Kloehr 858]

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 November 16, 2020 by John Kloehr

[Alpo 6,199]

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 November 16, 2020 by Alpo

[John Kloehr 858]

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 November 16, 2020 by John Kloehr

[John Kloehr 858]

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.

[Arizona Gunfighter 387]

I DON'T CARE!!!

[Noz 1,856]

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

[Forty Rod SASS 3935 6,844]

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 November 16, 2020 by Forty Rod SASS 3935

[watab kid 969]

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 , 

[Sedalia Dave 11,889]

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

  1/2 sphere with no top = 2094.395 Cubic cm

 

Area 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 November 16, 2020 by Sedalia Dave

[J-BAR #18287 5,721]

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.

 

Edited November 16, 2020 by J-BAR #18287

[Texas Lizard 1,059]

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

[Marshal Mo Hare, SASS #45984 6,843]

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

[MizPete 1,253]

Y'all are seriously making my head hurt.

[Alpo 6,199]

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

BS, MS, PhD

Bull poop and Mule poop, piled higher and deeper?

[Marshal Mo Hare, SASS #45984 6,843]

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 November 16, 2020 by Marshal Mo Hare, SASS #45984

[Chickamauga Slim 335]

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.

[sassnetguy50 290]

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?

[Captain Bill Burt 2,989]

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

[Alpo 6,199]

1 hour ago, Chickamauga Slim said:

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

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

[Chickamauga Slim 335]

3 hours ago, Alpo said:

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

It is a typo,

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

[Dirty Dan Dawkins 889]

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

[Colorado Coffinmaker 3,341]

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

[John Kloehr 858]

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 November 16, 2020 by John Kloehr
Auto correct failed

[Noz 1,856]

4 hours ago, sassnetguy50 said:

What size are your rows?

Whatever the planter pulled behind the mules measures.

[Captain Bill Burt 2,989]

2 hours ago, Chickamauga Slim said:

It is a typo,

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

Then .449

Edited November 17, 2020 by Captain Bill Burt

[Imis Twohofon,SASS # 46646 1,949]

Pie are round, cornbread are square

 

Imis  and a nod to Justin Wilson

[DeaconKC 1,269]

@Alpo  my head hurts from this....