pardon the dumb question, but why is a circle's circumference 3.14 times its radius squared? i mean why exactly 3.14? why not 3 or 4? why 22/7? couldn't it be 21/7 or 28/7? shouldn't it have been a multiplication of two or five or ten, numbers which seem to be repeated a lot in our daily lives? where did 3.141..... come from? how can such a hard to quantify number have such importance in the geometry of the known universe? or did we create our numbers scale wrong to begin with, and that's why it's hard to express pie in it? maybe have we chosen our counting system more carefully, pie would've come a simple multiplication of one of its numbers or something.. how pie fits clumsily as a number and snugly in our univers's geometry is beyond me.
It isn't. Because it has the value it has. It just is. The questions just get dumber. It just is, it didn't 'come from' anywhere. Maybe there's a clue there? There's a word, 'scale'. Pi would have the same value regardless of number system, base, or expression. Clumsy? No. Beautiful, yes; \( e^{i\pi} = -1 \)
Well, to begin with, it seems the biggest problem here is that you simply don't know what pi is - and it is "pi", not "pie." And the formula you stated is NOT the one for the circumference of a circle but the area of a circle. 2 pi R or pi D gives the circumference. And you also contradict yourself by first saying "exactly 3.14" and then later indicating that it's not "exact" - which is correct since it's an irrational number. Pi is simply a ratio - and ratios just turn out to be whatever they are. For example, what is the ratio of the distance between London and Paris compared to the distance between the North and South Poles? I sincerely doubt it would work out be an exact whole number - which is what you would seem to want it to be.
I'm just about to have a cup of coffee... Some "pie" would be nice..Please Register or Log in to view the hidden image!
I think this thread defies...everything, pretty much. Why isn't pi 22/4? Why is gravitational acceleration 9.8m/s2? Why isn't the moon made of blue cheese?
The moon isn't made of blue cheese?.. What's next? Gonna tell me there's no God? Oh wait...Please Register or Log in to view the hidden image!
Yep. I think we're talking to a very young person here - kids always expect everything to be perfect. Please Register or Log in to view the hidden image! I wonder if he would rather pay $20 for something rather than $17.95? Please Register or Log in to view the hidden image!
Aside from the various spelling and math errors in his post, it is actually a legitimate question. Just like the force of gravity on Earth, the speed of light, and many other mathematical laws in the universe, they all derive from something. And, very few are whole numbers. It is the whole number that is an anomaly, not the things it describes. Few if any key ratios or formulae result in nice and tidy whole numbers. Changing our numbering system (say, to a base 6 rather than a base 10) might convert one importation formula or ratio to an expression that results in whole numbers, but others would not. If there WAS a numbering scheme that could actually turn the whole of physics and geometry into exercises of whole numbers, I think you would have the makings of a Ph.D. in math...
Maybe some kind of set math.. that stuff scares me. Nothing in set math can have a value of 1 and such, they just assign a number to the set even if its value is zero. It would be interesting to apply set math to physics or other new maths, just count me out I tried studying up on it and it was like studying quantum mechanics all over lol. No offense QM guys its just not my cup of tea.
No it isn't. There is absolutely NO value in wondering why it has the value it does. It just does. Did you not see the formula I posted? It's significance is lost on you, is it?
It's a good thing none of the great scientists and mathematictions of mankind shared your outlook; we'd never figure anything out. Did you not see the phrase "the whole of physics"? It's significance is lost on you, is it?
Please Register or Log in to view the hidden image! Sometimes a circle is just a circle. Please Register or Log in to view the hidden image! Seriously though, I think if you computed π using the integration of, say, isosceles triangles, then it would make more sense.
I used to be a scientist. There is no value in pondering the significance of the value of these things. Discovering the values, improving accuracy, using the numbers to make predictions, yes. The actual value? No. So that formula was wasted on you.
Okay, to begin with, we can easily see that π is greater than zero and less than infinity. This doesn't help much, but it's a beginning. Looking at a circle, we know they say π equals the circumference divided by its diameter. Let’s make this easy on ourselves and make the diameter equal 1 — in that way, the circumference will (supposedly) equal π. We can then talk about and compute circumferences and perimeters that will be right around π. If we enclose the circle in a box, the box’s perimeter measures exactly 4, because it's as high and wide as the diameter, which is 1, so the box's perimeter equals 1+1+1+1 = 4. If we place the biggest box possible inside the circle, we use Pythagorean’s Theorem to see that each of its sides equals √([½]²+[½]²) , which gives the box a perimeter of 4√½, which equals about 2.8284271… . So, now we know π is less than 4 and greater than 4√½. So, we now know it can't equal 28/7 (=4) as was suggested. We could continue by using 8-sided figures, 16-sided figures, etc, and the perimeters of these polygons (are tougher to compute) and would converge on a value equal to 3.14159265358979… otherwise known as π. It turns out that (so they say) the ratio of the circumference to the diameter cannot be a ratio of two whole numbers. However, if you want to use a ratio of whole numbers that's far more accurate than 22/7, try 355/113, which is only off by about 85 billionths (85/1,000,000,000).
I think the OP asks a decent philosophical question and the first few responses are rude and stifling. Two points: 1) pi = 1 with the appropriate radix (bases don't have to be integers) 2) I believe pi could take on any value we wish with dimensional curvature Please Register or Log in to view the hidden image!
I think once you are convinced that such a ratio should exist, then there is no question of why the ratio must have such and such value, because it is just the value of the ratio, whose existence we are convinced of.
Not in the least. There's a TREMENDOUS difference between philosophy and solid mathematics. Just as a ratio is whatever it is - some number - math is just math and is neither rude nor stifling. As i said before, I believe we're just dealing with a very young person who wants everything to be simple and work out in whole numbers.Please Register or Log in to view the hidden image!
