Forgot to answer this one while I’m on the computer, what I meant by make ovals calculable is that currently (to my knowledge at least) there is no means of calculating the perimeter/circumference/border of ovals, likewise there is no means of calculating the area, without these measurements even if one wanted to try and find a relationship with PI (which I doubt there is, more likely just like right angled triangles it depends on width & height being the same to get a consistent number), what I’m aiming to do is remove PI from the equation to get a universal law which applies to all curves, circles & ovals would just be an extension of that, the key to that law is the number of sides, 2nd is currently square root to get the length between a and b xy points, the rest should be just addition or multiplication (the multiplication I’ll aim for after getting the addition correct)
A point I completely forgot to respond to:
These communities are not going to transition from using the actual functions to using approximations of them
I’m not expecting them too, the method for drawing a curve of any kind is more accurate then anything PI can produce, and possiblly trigonometry too, plus it’s fast. As for border length and related values I’m not expecting them to use my method until I actually perfect it, then it will be 100% accurate for the number of sides specified, that is what I’m aiming for with the new methods, the other expectation is that math that involves PI is gradually replaced with more accurate math born from the discovery of how to draw a curve without an infinity number like PI, in other words give computers something they can actually work with rather than an incomplete/inaccurate version of PI
The thing you’re trying to perfect is mathematically impossible. At least 2 millennia of people have tried to do what you’re doing, and their conclusion has been that it is mathematically impossible. It’s been proven to be mathematically impossible.
There is no finite, rational math function that can compute the points on a circle. Period. You can get arbitrarily close, but only with arbitrarily many terms. Thousands of years of mathematicians are not stupid.
Similarly:
Computing the length of the hypotenuse of a right triangle from the length of the other two sides is mathematically equivalent to computing the square area of a circle. That’s called “squaring the circle”. That’s also a thing that has been proven to be impossible with purely geometric math (not unsurprisingly by the same thing I just linked to, since as you have “discovered” these are just rearrangements of the same problem).
Saying “as soon as I can square the circle, I’ll have a closed, rational way to compute circles” is like saying “as soon as I travel faster than light, I’ll have a way to get to other planets quickly”. I mean yes, that’s true, but it’s also a thing that isn’t going to happen.
Given that I’ve already gotten as close as 99% roughly and have only one more value to find a way to calculate (incidentally I found a way of getting that border value faster with what I have, still no PI, still no trigonometry), I’d say your wrong. Anything that has precision can be computed, it’s not mathematically impossible, as I’ve said before the values are intrinsically linked to the number of sides given to the curves, circles and ovals. Just because something is difficult, doesn’t mean it is impossible, for example, any invention when first created is difficult to make, but time tends to make that process easier and easier, one just has to refuse to believe something is impossible just because no one’s ever done it before.
1 + 1 cannot equal 0. That is impossible because of the nature of the numbers 1 and 0, what it means to add numbers, and what it means for two numbers to be equal.
What you are positing is equally impossible. It’s less simple to explain why it is impossible. But it’s no less impossible for involving more complex mathematics.
This is irrelevant, since we already know that you can approximate circles with finite math. You can approximate circles with arbitrary precision with finite math, given arbitrary numbers of terms. You can get an answer that is as precise as a float can store. Or even a double.
But that answer will not be correct. You’re claiming to want to get an exact number, and you never will.
… Do you know what “transcendental” means? It means (put very simply) that it has infinite precision, and therefore cannot be computed by any finite device.
infinite precision is STILL precision, just because a device runs out of bits to store it and stops recording does NOT mean it cannot compute it, just means the result given will be within the bits allowed which is not infinitely accurate. Anyways I’m trying to implement the PI version for comparison (I also want to compare the xy points of each so I do need the individual values) but I’m not getting anything drawn to context, I’m assuming I’ve misunderstand the method or something because this isn’t working:
var radius = (width / 4) + (height / 4)
, half = sides / 2
, stop = sides / 4
, middle = stop / 2
, scaleX = 1 / pxWidth
, scaleY = 1 / pxHeight
, sizeX = 1 / 40
, sizeY = 1 / 40
, div = 1 / stop
, frac = div / stop;
...
for ( var i = 1, x = 0, y = 1; i < stop; ++i )
{
var xy = x + y;
var X = xy * scaleX * width, Xp = (X + sizeX), Xm = (X - sizeX);
var Y = xy * scaleY * height, Yp = (Y + sizeY), Ym = (Y - sizeY);
...
x += frac;
y -= frac;
}
Do you mind correcting me my method?
It, in fact, cannot, because it would require infinite time.
Time is just a variable, not the ability itself, it’s perfectly possible to have a computer start the calculation and never stop, it’s perfectly possible to just have the numbers display on screen offset to the set currently being worked on, what you’re saying is that we cannot do that, people have turned on linux machines and never turned them off just to see how long it will last, sooner or later someone will just set an algorithm to calculate PI but never stop by simply throwing away the upper bits that have been calculated and continuing on with a blank slate