Reading A Book "The Man Who Counted"

[denrep]

Tomorrow, Alfred's heading downtown to the big round tiled rotunda of the courthouse building, with a parking-lot stripe painter, chalk-line, and 70' tape measure.
We're gonna settle this.

[William McCormick]

Stop right there. To be clear,I didnt arbitrarily select a random number for any dimension. I started with the given chord length of 70. Knowing that the circles share a common center I split half of the chord in half, so that any centered dimension would "mirror" or have a symmetrical twin.

Who else has what way?

How 'bout it WM, what's your way?

My math teachers used to make me inhale the graphite dust, while I was sharpening pencils and wearing the dunce cap which was most of the class. I could hold my breath for well over 2 minutes I would back away and breath. Some of my comments while wearing the cone of wisdom as I preferred to call it, were historic. Many got me sent to the office where they actually got a kick out of me. I would come up with things like this a circle with the diameter of 70 units, has the same area as any disk with a hole in the disk and a 70 unit chord, that intersects, the circumference of the hole in the disk, at a single point tangent to the holes circumference. There was just no way left to punish me. A couple times I just winged things like this and nailed it, while I was sharpening pencils and making distracting noises. The teacher would just stand there and check it out on the chalk board shaking her head not in awe, but rather resentfully perhaps cursing my parents for having me. I would use extremes opposite end of the spectrum tricks to come up with quick answers. The class just thought I was an arrogant fool, rather then a rebellious future leader. What did they know? Ha-ha


Sincerely,

William McCormick

[MinnesotaDave]

Tomorrow, Alfred's heading downtown to the big round tiled rotunda of the courthouse building, with a parking-lot stripe painter, chalk-line, and 70' tape measure.
We're gonna settle this.

Now that's funny

Overkill - but funny

[sacherjj]

sacherjj
the point i was trying to make is that, under a microscope (powerful as you dare imagine), the shapes, measurements, and numbers we use to represent them, all end up under the classification of irregular.

the universe is filled with irregularity which to me says, we dont know how to describe.

math is enough to build structure with, and cars, but if we could describe what is naturally occurring, as in what shapes make up dirt, what shapes make a tree (the word shapes sounds funny here but its the best i have), we would be that much further ahead.

But we DO describe it. Math doesn't have to be a formula. We have collections of numbers that map the surface of the earth. Topomaps. We could measure a tree in 3D space very accurately. I agree that the world has such variation that we will never have a formula to generate it. However, we can measure and generate a representation of something good enough to get things done.

a 2 dimensional circle (or 3 i dont care) turns on it's center. rotation is shown with an arrow on top pointing right, and an arrow on bottom pointing left(clockwise). surface speed decreases as you near the axis of rotation, and increases again as you pass it. so mathematically, there should be a surface speed of zero at the axis. but most call that impossible and say the circle as a whole, must have some sort of rotational speed at any given point.

you tell me, does the circle stop in the center? or is the idea of a central axis impossible. you can roughly illustrate this when facing a shaft on a lath. start at the bottom, the right side of the cutter is cutting. get to the center, and hypothetically no cut, if possible to truly find it. and as you pass it, the left side of the cutter is working

You are talking a disc, since a circle is an infinitesimally thin line that bends. If the idea of a central axis was impossible, then we could never have a wheel that was balanced. The central axis is defined by the lathe when you cut. It is impossible to have a point without tangential rotational velocity, because atoms have some size. So even if the perfect center of the rotating disc fell on the center of an atom, one side of the electron cloud would have rotation in one direction and the other side opposite.

just bugs me

Why? Math is theoretically perfect description and the world is more complex. So build a model that is close, deal with the tolerances that they don't align, and move on. What other choice do we have?

[weldinghomer]

The general case is interesting. The area is always just pi * (chord length/2)^2

[MinnesotaDave]

The general case is interesting. The area is always just pi * (chord length/2)^2

I found the same - it is an interesting result.

My brother would just say "esoteric" and shake his head when I say stuff like that

[denrep]

...My reasoning is like this.

Take any circle you like. I can put a chord line on it 70 units long. Then I can put an inner circle on this that is tangent to the chord line.
So if it is possible to construct many different scenarios adhering to the given info then there is no solution.

Today I thought about Homer's reasoning, and I was just checking in to surrender and agree that it couldn't be done. After surrendering I was gonna check the book or web for a possible solution. But I had really wanted to 'cipher it on my own.
...I never thought of a constant.

Doesn't seem possible to the eye.
Strange phenomena.

McCormick - Don't you have a book of cocktail party jokes, or something?

[MinnesotaDave]

Today I thought about Homer's reasoning, and I was just checking in to surrender and agree that it couldn't be done. After surrendering I was gonna check the book or web for a possible solution. But I had really wanted to 'cipher it on my own.
...I never thought of a constant.

Weldinghomer was incorrect - but changed his position in post #80.

Multiple sizes that all yield the same area is a valid result to a very unusual question.

[denrep]

Right.
But I had decided to surrender before seeing #80.


And how long was the poor beggar who figured that out shackled in solitary with nothing else to do?

[MinnesotaDave]

Right.
But I had decided to surrender before seeing #80.

Here's another one:

Two circles share a common center point.
The larger circle has a circumference 10" larger than the smaller one.
What is the distance between the edges of the circles?

(More specifically, what is the difference of the two radii?)

[denrep]

With a quick easy test using diameter 20 (r10) looks like small diameter +pi = large dia.
Does that stay constant?

[weldinghomer]

10/(2*pi) ??

[MinnesotaDave]

10/(2*pi) ??

Bingo

And it'll be the same result no matter what inner circle size a person starts with

[Insaneride]

Im sure Bif and ED know what a Sine is. Its what they do to cash there check on Fridays. A CoSine is when two people have to sine there checks

Seriously tho, if they havnt painted that carousel by now, I would be looking for different painters.

[MinnesotaDave]

Im sure Bif and ED know what a Sine is. Its what they do to cash there check on Fridays. A CoSine is when two people have to sine there checks

[Insaneride]

You got me
Now Im going off on a tangent

[MinnesotaDave]

You got me
Now Im going off on a tangent

[Insaneride]

I think I was setup for that one MDave

[MinnesotaDave]

I think I was setup for that one MDave

The probability is very close to 1.0

[William McCormick]

Here's another one:

Two circles share a common center point.
The larger circle has a circumference 10" larger than the smaller one.
What is the distance between the edges of the circles?

(More specifically, what is the difference of the two radii?)

The circumference would normally be decided by the diameter through multiplication, pi times diameter equals circumference. So if you took the 10 inch circumference difference, and divided it by pi you get 3.1830988618379067153776752674503 which is the difference of diameter of the smaller circle, and the larger circle. If you divide that in half, you get 1.5915494309189533576888376337251 the difference in radius between the two circles, which is also the difference in distance between the circumferences of the two circles, or the edges of the two circles.

This is based on pi being 3.14159 to which I disagree but it is close enough.

Sincerely,

William McCormick

[William McCormick]

Denrep how many cocktails does it take to get laid?


One but watch out for their spurs.


Sincerely,

William McCormick

[William McCormick]

If you asked a women that you really liked, a women that also baked an amazing pie, if you could lay a chord, up to her pie hole, and then lay a cucumber standing up perpendicular, from her pie hole and your chord, out to the edge of her pie crust.

Are you?

A. A mathematician,
B. A perverted mathematician.
C. A virgin attempting to use the circular segment formula to measure her pie
D. A red dot on the sex offender map



Sincerely,

William McCormick

[Insaneride]

Now thats a tangent

[William McCormick]

But we DO describe it. Math doesn't have to be a formula. We have collections of numbers that map the surface of the earth. Topomaps. We could measure a tree in 3D space very accurately. I agree that the world has such variation that we will never have a formula to generate it. However, we can measure and generate a representation of something good enough to get things done.



You are talking a disc, since a circle is an infinitesimally thin line that bends. If the idea of a central axis was impossible, then we could never have a wheel that was balanced. The central axis is defined by the lathe when you cut. It is impossible to have a point without tangential rotational velocity, because atoms have some size. So even if the perfect center of the rotating disc fell on the center of an atom, one side of the electron cloud would have rotation in one direction and the other side opposite.



Why? Math is theoretically perfect description and the world is more complex. So build a model that is close, deal with the tolerances that they don't align, and move on. What other choice do we have?

If, you believe there are particles of elelctricity orbiting the hydrogen atoms the hydrogen atoms that make up all atoms. The only difference between steel and helium is the number of hydrogen atoms each contain.

Math is effected by temperature, humidity, rain, sunshine. Math is worse, and more finicky, then your old lady during her cycle. If you take an I-beam measure it to 20 feet, outside on a brisk January New York City day, come July your I-beam measured exactly correct to 20 feet, will be found to have grown to 20 feet and 1/8" inch. Now if you had 8 of those end to end, your building just grew an inch. Or buldged out an inch over the foundation. If you had 24 of them end to end your building grew 3 inches. Math is a great tool it is as stupid as a hammer though.

Sincerely,

William McCormick

[Insaneride]

Hydrogen has one electron in its valence band. Helium has two electrons in its valence. There is no hydrogen in helium. Steal is made from Iron and carbon. Iron and carbon are both atoms but are not made from hydrogen atoms. Hydrogen in steal causes hydrogen imbritlement, not good because this causes cracks and failure. Modern steal can contain additional atoms like Vanadium for strength and Niobium for stability but no hydrogen.