Is π wrong?

[Jarvitä]

Ever wondered why the overwhelming majority of formulae involving the number pi seem to involve doubling its value? The solution is obvious.

http://www.math.utah.edu/~palais/pi.pdf

[math]2*\pi=\pi\mskip -7.8 mu \pi[/math]

 

[insane_alien]

pi is the ratio of the circumference to the diameter, simple measurements show that it is infact correct.

doubling pi is usually to do with us taking the radius. as the base unit instead of the diameter.

both routes are mathematically equivalent and it reallly just comes down to convention.

 

[Izack]

That explains why 360° = 2π rad.
Problem is...I already memorised the current π to 40 significant digits, and I don't want to relearn it as 6.284-whatever. :lol:

 

[Jarvitä]

pi is the ratio of the circumference to the diameter, simple measurements show that it is infact correct.

doubling pi is usually to do with us taking the radius. as the base unit instead of the diameter.

both routes are mathematically equivalent and it reallly just comes down to convention.

Diameter itself is a derived unit - double the value of the radius. Therefore, if mathematics is to be done in elementary units, the number pi needs to be doubled. How else can you explain requiring two units of angle to complete one circle?

 

[streb2001]

I already memorised the current π to 40 significant digits, and I don't want to relearn it as 6.284-whatever. :lol:

Try memorising the whole of Monty Python's cheese shop sketch instead. That would get you invited to more parties I think!

:rofl:

 

[to be]

Diameter itself is a derived unit - double the value of the radius. Therefore, if mathematics is to be done in elementary units, the number pi needs to be doubled. How else can you explain requiring two units of angle to complete one circle?

Who's to say radius isn't derived by halving the value of the diameter? It is all arbitrary, although it is indeed common to use 2 pi.

 

[MeDiCS]

An engineer, a physicist, and a mathematician are shown a pasture with a herd of sheep, and told to put them inside the smallest possible amount of fence. The engineer is first.

He herds the sheep into a circle and then puts the fence around them, declaring, "A circle will use the least fence for a given area, so this is the best solution."

The physicist is next. She creates a circular fence of infinite radius around the sheep, and then draws the fence tight around the herd, declaring, "This will give the smallest circular fence around the herd."

The mathematician is last. After giving the problem a little thought, he puts a small fence around himself and then declares, "I define myself to be on the outside!"

This should clear things up a bit :rofl:

 

[Hielor]

The diameter of a circle is something that you can measure directly, given just the circle itself and a measuring tool.

Measuring the radius requires at least two steps.

 

[tori]

Measuring stuff has nothing to do with mathematics. The point is that someone in the past has made an arbitrary decision and as a direct result we have to use 2π almost everywhere, while we could have just as easily used just π had he decided otherwise. You can see it clearly on the 3rd page of that PDF - things become much more logical and consistent with the rest of mathematics.

Thanks Jarvitä for the thought - and thanks for the latex macro.

 

[Jarvitä]

The diameter of a circle is something that you can measure directly, given just the circle itself and a measuring tool.

Measuring the radius requires at least two steps.

Constructing a circle, on the other hand, requires a radius. Measuring things is an engineer's job, not a mathematical task.

Besides, [math]\pi\mskip -7.8 mu \pi[/math] makes a lot more sense in terms of angle units and just about every trigonometric equation.

 

[kwan3217]

http://xkcd.com/567/ - Sure, we could stop dictators and pandemics, but we could also make the signs on every damn diagram make sense.

Also, a gram should be the mass of one liter of water, and one meter should be the length of the side of a liter cube.

And why is the fundamental unit of time, the primary base of all our measurements, and the thing we can measure the best, called the second? Why not first?

 

[Hielor]

Measuring stuff has nothing to do with mathematics. The point is that someone in the past has made an arbitrary decision and as a direct result we have to use 2π almost everywhere, while we could have just as easily used just π had he decided otherwise. You can see it clearly on the 3rd page of that PDF - things become much more logical and consistent with the rest of mathematics.

Thanks Jarvitä for the thought - and thanks for the latex macro.

Measuring stuff has everything to do with the value of π. It wasn't an "arbitrary decision" when the concept came along. They had physical circles and physical measuring devices, and the convenient thing was to have the ratio be between two measurable quantities.

Plus, what calculations using π would have been most common? Other than the obvious one(ratio of one measurable quantity to another), I would think that area of a circle and volume of a cylinder would be the most common, and both of them would require the addition of a 1/2 if π were double its current value.

 

[Andy44]

And why is the fundamental unit of time, the primary base of all our measurements, and the thing we can measure the best, called the second? Why not first?

:huh:.....runs to get duct tape to wrap head and prevent explosion

 

[statickid]

this paper is meaningless to me. The beginning of the paper says that it is an opinion paper, the first section of the paper claims that most people would shout blasphemy at their so-called discovery.

This is a classic way of making non-thinking people agree with you. Its hilarious because by starting an argument this way, the writer is setting up all who who disagree as religious lunatics who refuse to see anything in a new light or accept new information.

The reason that radians measure out 2Pi is because it is based on radius and the unit circle. the definition of pi is a ratio of diameter of circle to circumference. There is nothing that inherently makes measuring the diameter more accurate or less accurate than measuring the radius. All of their ratios will remain the same. radians are derived from the "unit circle" which has a radius of 1 and it is incredibly useful. This person who wrote this wants to sensationalize non-information and pretend that they have discovered new information.

Additionally this does not streamline or redefine any processes, it does not bring any new understanding, it is the illusion of progress presented in double talk and empty semantics. From now i'm going to write the word "poop" instead of the letter pi but my math will all be the same.

 

[NukeET]

:huh:.....runs to get duct tape to wrap head and prevent explosion

Would you post that video on YouTube please?

 

[Xyon]

And why is the fundamental unit of time, the primary base of all our measurements, and the thing we can measure the best, called the second? Why not first?

In 1267, the medieval scientist Roger Bacon stated the times of full moons as a number of hours, minutes, seconds, thirds, and fourths (horae, minuta, secunda, tertia, and quarta) after noon on specified calendar dates.[7] Although a third for 1⁄60 of a second remains in some languages, for example Polish (tercja) and Turkish (salise), the modern second is subdivided decimally.

http://en.wikipedia.org/wiki/Seconds#Before_mechanical_clocks

To explain a second, we need to start with a minute. The word minute was derived from Latin and carried the notion of a small interval. When you divide an hour into 60 equal pieces, you get a very small - or "minute" (as in, accent on the SECOND syllable) - length of time.

The word second is short for "second minute," meaning a second division into small pieces (60 again), a sort of second order of minuteness. A second was considered a very short time indeed.

http://www.boston.com/news/science/articles/2009/02/23/in_time_why_are_seconds_called_seconds/

 

[Andy44]

Would you post that video on YouTube please?

Well, here's what happens if I don't duct tape my head in time, courtesy of Michael Ironsides (WARNING: GRAPHIC 1970s HORROR CLASSIC):

http://www.youtube.com/watch?v=HY-03vYYAjA