# Near equalities....

by AlbertEinstein
Tags: equalities
 P: 113 Mathematics usually contains a few coincidences which themselves give an account on how thrilling and exciting mathematics is. Here I have started a new thread whisch enlists some near(or very near equalities. Hope you guys would extend the thread! 1. We all know the near equalities of pi such as 22/7 ,355/113 etc (which are a result of continued functions).But do you know :Write 1234 as 2143 and then divide 2143 by 22. NOW take the 4th root of the result(i.e. take the sqrt and again take the sqrt).Isn't the number which you get now tantalizing close to pi ! pi^4 ~ 2143/22where ~ denotes near equality. 2. 3^2 + 4^2 = 5^2 from the old pythagoras theorem , but do you know 3^3 + 4^3 + 5^3 = 6^3. Exciting!
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,902 You have a very strange idea of what "thrilling and exciting" are!
 P: 131 The one that pops to mind for me is the expression: $$e^{\pi\sqrt{163}}$$ This value is very nearly an integer. But, not quite. The value is: 262537412640768743.99999999999925007259... If you type the above expression into a non-graphing calculator, the result will come out as an integer because the number of 9's exceeds the calculator's floating point abilities.