Without using meme, incommensurable numbers like [math]\pi[/math]

>>8797494
circles don't exist irl

shitty b8

>>8797497
By real circles I mean things which we would say are circles but actually aren't on a microscopic level. Think pixel art circles.

>>8797498
No, I'm serious, I want to stop using [math]\pi[/math] and other irrationals.

>>8797494
>What's the formula for finding the area of a real circle
I don't know the formula, but there is one.
How do you think people calculate pi to a zillion digits?

Here's a simple start with geometry:
>draw a circle with a radius of 1 unit length
>draw a square with sides of 2 unit lengths such that the center of each side just barely touches a point on the original circle
>draw a square with sides of length such that each corner just barely touches a point on the original circle

The larger square is larger than the circle, and has an area of 4 square unit lengths.
The smaller square is smaller than the circle, and has an area of 2 square unit lengths.
The circle's area is smaller than 4 and larger than 2.
Repeat with polygons with more sides.

Checking in ms paint it goes like this.

3:1
4:4
5:9
6:12
7:21
8:32

Diameter in pixels on the left and area in pixels on the right. I'm sure there's a pattern there somewhere. Couldn't be arsed to do more.

>>8797494
Is this squaring the circle?
Then subtracting the known ratio of the corners area from the area of the square.

>>8797541
Odd and even circles in pixel/graph will have different centers.
1 block for odd
4 blocks for even
So.... good luck

>>8797494
Circles are a meme.

>>8797504
>By real circles I mean things which we would say are circles but actually aren't on a microscopic level. Think pixel art circles.

Circles are a mathematical object you mongoloid. They exist only in the realm of geometry, not in the real world.

>>8797537
REEE I can't work out the pattern.

>>8797504
Every circle is different, you can draw 10000 different circles and all their areas will be different. So there is no formula, the best you can do is approximate. That's why we use pi, because that's the best estimator of their areas. And we don't use all infinite digits of pi either, we only use let's say 100 digits

>>8797494
Measure the height of the circle.
Measure the width of the circle.
Multiply them together.
Multiply by 11.
Divide by 14.

>>8797494
>real circle
What is a "real circle"?

Because the standard definition (the set of all points with distance r from a point X) does not work.

Before you can actually tell us what you mean with "circle" we can not give you an answer.

>>8797494
>What's the formula for finding the area of a real circle
A=22r^(2)/7

>>8797567
I can make a perfect metal circle disk on a lathe. So yeah, they exist.

>>8797497
What about the circle of life? check and mate

>>8798110
>Perfect circle on a lathe
You must be blind anon...

>>8798110
Even assuming you perfectly center the workpiece, your chuck runs perfectly true, cutting tool is mounted perfectly stiff, that neither tool nor workpiece vibrate you won't get perfect circle because it won't consist of infinitely many points but only finitely many particles and they won't be exactly one radius apart from the center but their distance from the center may vary by some atomic distances

A real circle would be an object that has the approximate shape of a circle. Finding the area of this real object would be a matter of reconstitution of the object into a form that has a volume that can be measured and comparing that to the volume of a similar object that had the shape of a square (same thickness, and material.) one could also simply compare the mass of the before mentioned objects. Even some kind of optic mapping could work, count the pixels in a circle and the pixels in a square of known size and divide the circles pixels with the squares pixels and multiply by the squares (known) size. None of these are exact, but that is not really a problem since no real circle is exact. The optic map could just as well be done by bouncing sound waves on the objects in a grid, but the measurement of mass or volume are still the most real options. Paint a circle and a square on a window. once dried peel off the pain. Weigh the circle. Cut a two inch by two inch square of the same paint. Weigh it. The Area of the circle is weight of circle / weight of square * 4.

Do you mean something like this OP?
https://en.wikipedia.org/wiki/Midpoint_circle_algorithm

>>8797504
>By real circles I mean things which we would say are circles but actually aren't on a microscopic level.

You mean convex polygons. You could consider a circle a certain polygon where the number of sides are infinite. So it's a theoretical construct, because in reality (and with pixel art) that's not true.

You could do the same thing you do in computer graphics and similar fields. Look up algorithms for polygons.

>Think pixel art circles.
Pixel art circles are discreet. They are made of fixed units, there is no in between. They are extremely easy to count you basically need to count the outline and the pixels inside. Scanning and counting line by line can easily tell you. Look up common computer graphics algorithms.

PS: On the other hand I don't know why you don't want to use the tools provided by such a beautiful abstraction as a circle.

>>8798110
No, geometrical shapes are abstractions. What you're saying is like claiming you can find the number 12 in the world and pointing to a dozen eggs. This is not the same as the number twelve. If you don't understand that mathematical objects are formal, not material, you haven't understood mathematics at all.