Squared Circle

[Motor_Daddy]

@obsrvr524

If I just assume that those center lines are separated by one radius - I can calculate any of those areas.

The vertical center lines are exactly 1 radius apart, because the circle has a diameter of 2. The intersections of those line with the center horizontal line is 1/2 a unit from the center of the circle, and a 1/2 unit to the edge of the circle on both sides. The grid squares are exactly 1 unit x 1 unit, except for the outer left and right, which are exactly 1/2 unit x 1 unit.

[obsrvr524]

@Motor Daddy

@obsrvr524

That would be pretty easy except because of the way you drew it. Because you just guessed until it looked right - you can’t know exactly where those vertical center lines are.

I didn’t guess at anything. EVERY line is formed from an intersection. The corners of the square are the intersections of those crossing lines at the corners. Every line is dead nuts accurate with intersections.

Every line is point to point somewhere along those lines. They are all DEAD NUTS ACCURATE, no guessing involved.

I asked you how you placed the vertical center lines for the upper and lower circles - you said that you just kept adjusting. If that is not right - exactly what determined those vertical center lines?

[obsrvr524]

@Motor Daddy

@obsrvr524

If I just assume that those center lines are separated by one radius - I can calculate any of those areas.

The vertical center lines are exactly 1 radius apart, because the circle has a diameter of 2. The intersections of those line with the center horizontal line is 1/2 a unit from the center of the circle, and a 1/2 unit to the edge of the circle on both sides. The grid squares are exactly 1 unit x 1 unit, except for the outer left and right, which are exactly 1/2 unit x 1 unit.

Then my calculations should be right.

[Motor_Daddy]

@Ecmandu

Alright…

This is funny.

It’s just basic logic.

Let’s say you cut a string at 4 inches long.

You make a square that’s 1 inch * 1inch * 1 inch * 1 inch.

Then you take the same exact string and make a circle .

That’s how you square a circle.

The perimeter and surface area are exactly the same.

No, using your method the circle has a diameter of 4" (radius of 2) and the square’s sides are 4".

4 x 4 =16 square inches of area for the square
3.14159 x 4 ( which is pi(r^2) ) = 12.56636 square inches of area for the circle

[obsrvr524]

And that means that your areas are off by (3-\pi) = 0.14159265

[Ecmandu]

@Motor Daddy

@Ecmandu

Alright…

This is funny.

It’s just basic logic.

Let’s say you cut a string at 4 inches long.

You make a square that’s 1 inch * 1inch * 1 inch * 1 inch.

Then you take the same exact string and make a circle .

That’s how you square a circle.

The perimeter and surface area are exactly the same.

No, using your method the circle has a diameter of 4" (radius of 2) and the square’s sides are 4".

4 x 4 =16 square inches of area for the square
3.14159 x 4 (which is pi(r^2) = 12.56636 square inches of area for the circle

Now you’re talking about radius!

It’s incidental to the problem. Obviously a square NEVER has the perfect radius of a circle.

[obsrvr524]

@Motor Daddy

@Ecmandu

Alright…

This is funny.

It’s just basic logic.

Let’s say you cut a string at 4 inches long.

You make a square that’s 1 inch * 1inch * 1 inch * 1 inch.

Then you take the same exact string and make a circle .

That’s how you square a circle.

The perimeter and surface area are exactly the same.

No, using your method the circle has a diameter of 4" (radius of 2) and the square’s sides are 4".

4 x 4 =16 square inches of area for the square
3.14159 x 4 ( which is pi(r^2) ) = 12.56636 square inches of area for the circle

Ecmandu is confusing the area with the circumference - the areas have to be the same.

[Motor_Daddy]

@obsrvr524

@Motor Daddy

@obsrvr524

I asked you how you placed the vertical center lines for the upper and lower circles - you said that you just kept adjusting. If that is not right - exactly what determined those vertical center lines?

I never said anything of the sort. Provide the quote!

The left vertical line is a vertical straight line along the 2 vertical circle left sides. The right vertical line is a line along the right sides of the left 2 vertical circles.

See how those vertical lines run perfectly along the edges of those 4 circles?

[Ecmandu]

It’s not an area problem, it’s a radius problem.

[Motor_Daddy]

@Ecmandu

It’s not an area problem, it’s a radius problem.

The areas have to be the same.

[obsrvr524]

@Motor Daddy

The vertical lines closest to the center were arrived at by a series of straight lines until I had enough lines to run them vertically through the centers of the circles they vertically run though the centers of.

That sounded like guessing until you got what looked right. Later I figured out that the grid squares were 1 unit square and that allows for calculation.

[Ecmandu]

@Motor Daddy

@Ecmandu

It’s not an area problem, it’s a radius problem.

The areas have to be the same.

They are the same.

The problem is a pun…

You’re literally “cutting corners”

So in ideal forms… they are exactly the same.

When you work with physical reality, when you take a string and bend it into 4 parts, it angles and scrunches upon itself to make the square - which causes less surface area for measuring. Thus, the discrepancy.

In ideal forms, this physical problem doesn’t occur.

That’s circumference… that also impacts area calculations.

[Motor_Daddy]

@Ecmandu

@Motor Daddy

@Ecmandu

It’s not an area problem, it’s a radius problem.

The areas have to be the same.

They are the same.

The problem is a pun…

You’re literally “cutting corners”

So in ideal forms… they are exactly the same.

When you work with physical reality, when you take a string and bend it into 4 parts, it angles and scrunches upon itself to make the square - which causes less surface area for measuring. Thus, the discrepancy.

In ideal forms, this physical problem doesn’t occur.

That’s circumference… that also impacts area calculations.

For the circles area, we are talking about how much 2 dimensional space is in the circle. If the circle is filled with blue, it’s how much blue is in the circle. That is area. It is calculated by pi x (r x r).

So if your circle has a radius (distance from center to edge) of 2, then your circle has an area of 3.14159 x (2 x 2) = 12.56636 Square inches of area. That’s how much blue your circle will have.

[Motor_Daddy]

@obsrvr524

@Motor Daddy

The vertical lines closest to the center were arrived at by a series of straight lines until I had enough lines to run them vertically through the centers of the circles they vertically run though the centers of.

That sounded like guessing until you got what looked right. Later I figured out that the grid squares were 1 unit square and that allows for calculation.

Right, those grid squares are 1 x 1, and the grid is 4x4. The outer being 1/2.

So how much area is a blue piece and how much is red piece, according to your calculations?

[Ecmandu]

And there’s your problem.

I’m talking about 1 dimensional space.

In that, they have the same exact area.

Whenever you have to bend a line, the area will be different.

[Motor_Daddy]

@Ecmandu

And there’s your problem.

I’m talking about 1 dimensional space.

In that, they have the same exact area.

Whenever you have to bend a line, the area will be different.

1 dimensional space is distance
2 dimensional space is area
3 dimensional space is volume

examples:

1 dimension - the length of a stick
2 dimensions - the space inside a circle
3 dimensions - the space inside a beer keg!

[Ecmandu]

@Motor Daddy

@Ecmandu

And there’s your problem.

I’m talking about 1 dimensional space.

In that, they have the same exact area.

Whenever you have to bend a line, the area will be different.

1 dimensional space is distance
2 dimensional space is area
3 dimensional space is volume

examples:

1 dimension - the length of a stick
2 dimensions - the space inside a circle
3 dimensions - the space inside a beer keg!

Can we at least agree on the problem?

When you have to bend a line (to make a square) you lose circumference right there?

Can we agree on that?

That’s a physical problem.

[obsrvr524]

@Motor Daddy

@obsrvr524

@Motor Daddy

The vertical lines closest to the center were arrived at by a series of straight lines until I had enough lines to run them vertically through the centers of the circles they vertically run though the centers of.

That sounded like guessing until you got what looked right. Later I figured out that the grid squares were 1 unit square and that allows for calculation.

Right, those grid squares are 1 x 1, and the grid is 4x4. The outer being 1/2.

So how much area is a blue piece and how much is red piece, according to your calculations?

I calculated that a red piece would be - 0.05518971

So to get a blue piece -

@obsrvr524

The area of the purple portion of the square would be (4∗(0.5∗sin(60^o)+\frac{\pi}{12}))

Just subtract that from the circle’s area - (\pi) to get all 4 blue areas.

One blue area = (\frac{\pi-4∗(0.5∗sin(60^o)+\frac{\pi}{12})}{4})
~0.090586074

So the difference of blue-red ~ 090586074 - 0.05518971 = 0.035398163

[Motor_Daddy]

@Ecmandu

@Motor Daddy

@Ecmandu

And there’s your problem.

I’m talking about 1 dimensional space.

In that, they have the same exact area.

Whenever you have to bend a line, the area will be different.

1 dimensional space is distance
2 dimensional space is area
3 dimensional space is volume

examples:

1 dimension - the length of a stick
2 dimensions - the space inside a circle
3 dimensions - the space inside a beer keg!

Can we at least agree on the problem?

When you have to bend a line (to make a square) you lose circumference right there?

Can we agree on that?

That’s a physical problem.

A square has 4 equal sides. If you start with a 1" diameter rope, and try to bend it around to make a square, that’s a practical issue. We are talking theory, that is useful for talking of things without having to deal with mechanical issues.

It’s so we can talk about things as if it was a perfect world, which we know it isn’t. But it is very very very useful when applied to the real world.

[Motor_Daddy]

@obsrvr524

So the difference of blue-red ~ 090586074 - 0.05518971 = 0.035398163

So “close enough” is your call? Or would you call it “damn close?”