why does pi go on forever Explore the mathematical concept of Pi and its infinite nature through an in depth analysis on BBC Science Focus Magazine
While treating pi as equal to 3 14 is often good enough the number really continues on forever a seemingly random series of digits ambling infinitely outward and obeying no discernible Pi does not end and it never turns into a pattern of repeating digits e g 642642642642 It is the result of dividing the circumference of a circle by the diameter For a lot of numbers dividing gives you a simple result e g 6 3 2
why does pi go on forever
why does pi go on forever
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Pi is an irrational number like almost all other numbers and irrational numbers can t be expressed as finite sums of multiples of powers of 10 and since our writing system uses sums of multiples of powers of 10 it Is Pi Infinite Why When mathematician Johann Lambert proved that pi is irrational the fact that it is infinite came along at the same time The reason for this is that all irrational numbers are infinite Pi belongs to a group of transcendental numbers
The reason we can t call pi random is because the digits it comprises are precisely determined and fixed For example the second decimal place in pi is always 4 So you can t ask what the probability would be of a different number taking this position It isn t randomly positioned That s because pi is what mathematicians call an infinite decimal after the decimal point the digits go on forever and ever Students are usually introduced to the number pi as having an
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The digits of pi never repeat because it can be proven that is an irrational number and irrational numbers don t repeat forever If you write out the decimal expansion of any irrational number not just you ll find that it never repeats Therefore the digits of pi go on forever in a seemingly random sequence Pi is also a transcendental number which means no amount of mathematics could possibly determine its value
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why does pi go on forever - That s because pi is what mathematicians call an infinite decimal after the decimal point the digits go on forever and ever Students are usually introduced to the number pi as having an