Happy Pi day folks ! Heres a general misconception im having. It might turn out to be a pretty easy question so please do help me. If i pull out my compass to a radius of 7 cm and draw a circle on a paper. Then i'll take a piece of thread and cut it such that it matches exactly with the circle on paper and take the length of that particular thread and divide by 14cm, should i get the value of pi ? If its so, why isnt pi an irrational number. After all im dividing the circumfrence i've got by 14 cm. So it should a rational number. For example, if the circumfrence is 50.123456 cm ( i've not measured yet just an example) And i divide it by 14cm I shall get 50123456/14000000 as value of pi, which is supposedly rational ? Is it an contradiction ?
Happy Pi day to you too! (And welcome to PF!) (this is a message from the future … it's actually Pi-plus-one day here … are you in Alaska?) But your measurement won't be an exact rational number, will it? No matter to how many decimal places you try to measure it, you'll always find a little left over!
How would you manage to measure it to such precision? There are many reasons why an irrational number like pi will be approximated to a rational number with real world measurements. Hypothetically, it should be pi, but realistically, it's impossible to do.
You mean why is pi an irrational number. Or why isn't pi a rational number. No, a "measurement" is never exact. When you talk about "lengths" in geometry you are not talking about measurements.
Also unrealistic: - That the circle's radius is exactly 7 cm. - That this circle drawn with a compass truly is a circle.
Also - The thread perfectly tracing the circle. - The thread perfectly maintaining that same length after being stretched out straight. - The ruler being perfect. Even the thread's physical properties are limiting the perfectness of this imperfect exercise.