Winter at CWI, computes pi to 800 decimal digits. The following 160 character C program, written by Dik T. It can compute the Nth hexadecimal digit of Pi efficiently without the previous N-1 digits. This is how the Chudnovsky's have computed several billion decimals.Īn interesting new method was recently proposed by David Bailey, Peter Borwein and Simon Plouffe. This is why the constant 8k_4k_5 appearing in the denominator has been written this way instead of 262537412640768000. The great advantages of this formula are thatġ) It converges linearly, but very fast (more than 14 decimal digits per term).Ģ) The way it is written, all operations to compute S can be programmed very simply. It is the following (slightly modified for ease of programming): This gives a number of beautiful formulas, but the most useful was missed by Ramanujan and discovered by the Chudnovsky's. The disadvantage is that you need FFT type multiplication to get a reasonable speed, and this is not so easy to program.Ī third one comes from the theory of complex multiplication of elliptic curves, and was discovered by S. For instance, to obtain 1 000 000 decimals, around 20 iterations are sufficient. you double the number of decimals per iteration. They have the advantage of converging quadratically, i.e. In 1719, the French mathematician Thomas Fantet de Lagny had. A beautiful compendium of such formulas is given in the book pi and the AGM, (see references). In 1665, the scientist Sir Issac Newton had calculated the value of pi up to 16 decimal places. So, for any value of N, the count of N-digit palindromes will be 9 10(N 1) / 2. This gives about 1.4 decimals per term.Ī second is to use formulas coming from Arithmetic-Geometric mean computations. Approach: The first digit can be any of the 9 digits (not 0) and the last digit will have to be same as the first in order for it to be palindrome, the second and the second last digit can be any of the 10 digits and same goes for the rest of the digits. One of the oldest is to use the power series expansion of atan(x) = x - x^3/3 + x^5/5. There are essentially 3 different methods to calculate pi to many decimals. The current record is held by Yasumasa Kanada and Daisuke Takahashi from the University of Tokyo with 51 billion digits of pi (51,539,600,000 decimal digits to be precise). I am currently doing a little "math program" so i am researching.
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