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There is already the Feynman point in which there is a sequence of six 9's in a row. Anyway, who knows what we will find out there in the digits of Pi. The first 1,000,000 decimal places of pi were first calculated in 1973. 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. Comparison with this shows that the last three decimal places are wrong, so we have actually got pi correct to 1,000,101 decimal places. You need even fewer digits of Pi to get a uncertainty in the circumference smaller than the size of an atom. However, the uncertainty in the circumference is less than the Planck length-the smallest unit of distance measurement that has any meaning. If we don't know the exact value of Pi, but one 152 digits then we don't know the exact circumference. 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 years-it's complicated). If you know the diameter of this large sphere, you can also find the circumference using the value of Pi. If you still want to grok this Euler Identity, check out this site.
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You can say that 3 2 is like 3 groups of 3, but what about 3 1.32? Or what about 3 -3.2i? Those are pretty tough to picture. For me, the problem is that we like to think of numbers as real countable things. Therefore, from the above example, the value of pi is 3. However, that is sort of like explaining magic with more magic. Example: A circle has a circumference of 44 cm, its diameter is 14 cm.
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CALCULATE PI TO SERIES
Since the 1980s, his series have become the basis for the fastest algorithms currently used by Yasumasa Kanada and the Chudnovsky brothers to compute. Using the same method as for the pentagons, we get: Area of smaller polygon 1/2 x n x sin (360/n) Area of larger polygon n x tan (360/2n) where n is the number of sides of the polygon. Found several rapidly converging infinite series of, which can compute 8 decimal places of with each term in the series. Of course, you could use Euler's formula for exponentials: We can generalise the method we used to find the pentagon areas to enable us to quickly calculate the inner and outer polygons for any number of sides. Without the number zero, you really can't have place value so you are stuck with a number system like the Roman Numerals.īut why does this equation work? That's not such a simple answer. It may seem silly, but multiplying by one is very important-just take unit conversions as an example. With this number (the square root of negative 1) we can write complex numbers (combination of real and imaginary). This number is very important in calculus and other things ( here is my explanation from before). It makes a relationship between these five numbers: But calculating the digits of Pi has proven to be an fascination for. If you don't think that equation is crazy and awesome, then you aren't paying attention. Pi is a name given to the ratio of the circumference of a circle to the diameter.