But why does this equation work? That's not such a simple answer. Of course, you could use Euler's formula for exponentials:. However, that is sort of like explaining magic with more magic. For me, the problem is that we like to think of numbers as real countable things. But you can't count an imaginary number. You can say that 3 2 is like 3 groups of 3, but what about 3 1. Or what about 3 Those are pretty tough to picture. If you still want to grok this Euler Identity, check out this site.
Imagine a large sphere. If you know the diameter of this large sphere, you can also find the circumference using the value of Pi. Now replace the sphere with the diameter of the observable universe at 93 billion light years yes, I know this is bigger than 13 billion light yearsit's complicated. If we don't know the exact value of Pi, but one digits then we don't know the exact circumference. However, the uncertainty in the circumference is less than the Planck lengththe smallest unit of distance measurement that has any meaning.
You need even fewer digits of Pi to get a uncertainty in the circumference smaller than the size of an atom. So, should we just stop looking for more and more digits of Pi? No, we need to continue the quest for a better appoximation of Pi.
Anyway, who knows what we will find out there in the digits of Pi. There is already the Feynman point in which there is a sequence of six 9's in a row. Put points together, and you can compose any shape you like, without any irrational numbers. Every object except the base-unit is a composite object, made up of discrete points. I recognize there will be lots of objection to this way of thinking about geometry. Those objections will be addressed in detail in future articles. Note: this GIF was taken from Wikipedia to show the supposed irrationality of pi.
There are concrete, actual circles, each of which is a composite object constructed by a finite number of points. There are no diameters that have a distance of 1. Obviously, this topic requires a lot more explanation and work, not just in geometry, but everywhere that the metaphysics of mathematics is mistaken.
First of all, this framework fully explains all of the phenomena we experience , and it loses exactly zero explanatory power when compared to standard Geometry. Furthermore, base-unit math is more logically precise than the orthodoxy. They cannot use an actual infinite decimal expansion. They are forced to arbitrarily cut off the magnitude for pi in order to use it.
Not so with base-unit geometry. Perfect precision is actually possible, since there are no approximations or infinite decimal expansions to deal with. This might not be a big deal right now, but as technology approaches the base-unit dimensions of physical space, it might actually make a big difference. As the base unit shrinks — or as the circle gets larger in diameter — the ratio of its circumference to diameter changes ever-so-slightly. These calculations are immediately practical, in the same way that trig tables are practical.
They are pre-calculated values that are applicable and accurate for a given circle of a given size. If you want to understand why pi changes slightly, think of it this way: as the size of the base-unit increases, the area enclosed by the circumference shrinks; as the size of the base-unit decreases, the area enclosed by the circumference increases, yet at a diminishing rate. The smoother the edge of the circle, the larger the area of the circle.
Think of it this way: any given photograph will contain a finite number of pixels. It will have a base-unit resolution. We might even run into the limits of the physical world. Physical space must have a base-unit , which means within our physical system, there is no smaller unit. Who knows — perhaps we could say true things about a different physical universe that has smaller base-units.
Space must have a base-unit, if motion is possible. A great example of base-unit phenomena is the fractal. Fractals make much more sense within a base-unit context. Consider this image:. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Asked 6 years, 8 months ago. Active 6 years, 8 months ago. Viewed 40k times.
There's no ending in the decimal representation. Add a comment. Active Oldest Votes. So regarding your last question: No! It took me exactly four days to return to the point where I started the circle.
So I think pi must equal 4. Did I do something wrong? If we can devise measurements of different kinds by geometric methods, why not also with the transcendental ratio Pi of the circumference to the circle? For instance, we have a plank measuring However, if we construct a figure with an ascending arm into which we make an even division of three parts, then drop these parallel segments onto the board below, the Man is the measure of all things. Devise a new system of measurement as we did with our If a circle of diameter d had one side sliced off like a flat tire such that the resulting perimeter was 3d, how long would that flat side be?
Really enjoyed the article and it gave me some things to think about. Initially I thought the answer would be simple… but it seems my geometry skills are insufficient. Depending on how accurate an answer you can accept, using some deductive reasoning reveals a shockingly close approximation.
For a semi-circle with a diameter of 1, the arc length is equal to Pi. Chord length can be calculated from a known angle and radius! So, now we've got a reasoned guess a and a calculated guess c… 2. How does this compare to the p we need of 3? Honestly, would love if someone could provide a more accurate means of determining this. I could not dredge up any correlations that were helpful without some other given measure. Who knows, maybe I bungled it entirely.
Not something I would have attempted to answer on a "help forum". I am not a mathematician and only in middle school, but I was just thinking. I think that pi must be as it is because it represents pure change, pure movement, and…going out on a limb here…that is the substance of the universe. We describe and measure our objectively-experienced universe using points and lines.
Rather, we are constructed, and ourselves construct, along the edges of the horizon of the curve; where it vanishes from our perception, we call that a point.
But pi, with its neverending irrationality, its purity of change, gives us the clue that, from a cosmic perspective, there are no point or lines. Just the great circle. If you go three dimensional, you simply can change pi by changing the angle relative to the radiuses, creating a cone.
Pi simply works in our physical world, but only up to a point — just like Einsteins theories work in the world we know -up to a point. Then pi ratios seem rather insignificant and limiting. Does pi literally define the relationship between dimension 1 and dimension 2 in our particular universe?
Otherwise the universe collapses? Is the pi for time dimension 2, where the circle has collapsed to a single dimension, so out and back circumference is twice the diameter which is just out but not back? Pi represents a mathamatical constant, an assumed agreed upon aspect of the physical world we live in.
The sun will rise every day. If you want to delve into theortical physics, though, you can arrive at different ways that things can work. That question justs confuses the human line of reasoning. Thats probably why the crop circle regarding that was placed there.
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