Is western math missing something?

Yes. You cannot also draw a circle. Maybe if humans had had 12 fingers, we then would have a different set of irrational numbers.

No, they'd be the same numbers in a different base (and still irrational) Jeff

It's like Tom Lehrer said, "Base eight is the same as base ten, if you're missing two fingers."

Short, sweet, and to the point! Excellent!

By saying western maths is wrong it is implied that something else is correct.

State your alternative proposal please.

Does it bother me? No, it doesn't.

For one thing, I have never had to know the exact area of a circle down to so many decimal places. Most of the time, a ballpark figure is all I ever needed.

Not sure that Eastern math or Southern math is any different at describing the concept. Moreover, we've done this before.... Circles do not exist

First of all, pi is not an infinite number. The area of a circle of radius 2 has a value and not infinity. The area of the 4 x 4 square has a value and the area of the inscribe circle will in no way be greater than that square. So there is an area value of that circle. You can consider some decimal place value of pi for practical purposes. Be realistic!

Yes. Let me add: Pi is an irrational number, which means that it cannot be expressed or written as a ratio (or fraction) of two integers. The common ratio, 22/7 (3 1/7) is only an approximation, accurate to a couple decimal places. Other ratios have been used to describe Pi more accurately, but none are or ever will be mathematically exact. Because Pi is an irrational number, you can write it down with an infinitely long sequence of numbers which never have a repeating pattern. In that sense, Pi is infinitely long but not infinitely large.

I liked the nature of the question being asked. It goes back to the roots of knowledge--"Why?". I liked also the earlier post which notes that we can measure area with circular units instead of square units. That comment set my mind turning some.

--JMM

Hi JMueller,

That actually is done, at least in the US where large conductors are measured in circular mils. Then, when you have to equate that to square wire, the square is somewhat inexact.

Tom

Yes, Tom. I have been an electrician since 1971, and why we use circular mils for the large wire sizes still puzzles me. (It may be a hold-over from the very "early" days??) --J Mueller

math is an abstract concept having meaning only because we give it meaning through logic in our head; much like a programming language. The output of each is interpreted by us, analyzed, and then a decision for action is made from the synthesization of known facts, experiences, intuition, and original output. That is what allows us to solve such problems as (zorbs+tint).q=zorbs.q+q(zorbs)(tint)+tint.q. So basically pi builds on top of enumeration, number theory, logic rules, etc in an abstract way (e.g. your understanding of infinity). The exact mechanisms of this are not well understood.

I personally believe there will be no definite answer on the operation of our brain. Any thoughts people?

Isn't maths a formal system of rules (that are defined), operating on axioms (that are recognised as such).

Some combinations of rules and axioms generate interesting (to mathematicians) results and some are even useful in modeling the physical world. Most of us have only studied maths that is directly applicable to physical problems and so think that's all there is, mathematicians think we've only touched the edges. It's weird that much of the abstract maths studied in the past turned out to be so useful to engineers. If you want some fun, explain to a mathematician that the Dirac function "proves" that Infinity times Zero equals One.

I agree 100% with your anwer.But I don't see, even for fun, why we should care to explain this to a mathematicien as long as engineers do use it all the time successfully in the digital world.

Hi,

It's not western math, it came from the Pythagoreans of ancient Greece or before them. As has been pointed out, Pi is not an infinite number, but has an infinite number of digits, each one having 1/10 of the significance of the one to it's left (it's an irrational number). Apparently it bothered the Pythagoreans as much as it bothers you!

Pi is not merely irrational, it's transcendental, i.e. it's not the root of any algebraic equation. √2 for example is irrational, but not transcendental, as it's a root of x² = 2.

Codey

Pythagorus was a man not a people. It also bothered the Chinese, who independently found pi using large circles and many squares of a known area.

Yes to everyone, and we think in such linear terms, do we not? I think it is possible that Pi has no solution and is possibly infinite. The same can be said about the theoretical square, but we tend to accept the properties of the square as axioms, and see Pi as a postulate.

I know, I know-just accept it for how we interpret it and be happy with that. Not the reason we all became engineers, I think. For the time being I'll interpret Pi as the maximum number of digits I can enter in my desk calculator and hope my small "circle of life" does not expand much.

Excellent topic!

Best Regards,

Ing. Robert Forbus

No, Pi has an exact value (it exists as a point on the number line of Reals), we can approximate a solution but an exact answer requires an infinite number of decimal terms. Jeff

This is over complex silliness.

Allow me to simplfy and restate the 'question'.

Q. 1/3 can't be expressed as a decimal. Is the sky going to fall?

A. So what?...it won't stop you cutting a cake or fletching an arrow!

I once saw an article (I don't remember where or when) that described a decimal numbering system that use reciprical primes at each place eg (point)(1/2)(1/3)(1/5)(1/7)(1/11).... rather than the normal (point)(1/10)(1/100)(1/1000)... This allowed you to write some fractions easily eg 1/3 as 0.0100 but made writing others eg 1/10 much more difficult. Well, I thought it was interesting anyway. Jeff

It is alla right. The area of the circle is not infinite but is known to a limited accuracy but the square is completely known with accuracy.Area of circle is accurate with given system of numbers we have at present, we know it can not be below and not greater than some basic numbers.

What we call '1" is some assumption and is a single unit. Another important use is "Measurement of angle in radians" . Sin(Pi/6) is equal to 0.5. So Pi is 6 times of the angle.

Actual difficulty is measurement of an Arc in multiples of linear dimensions. The accuracy is more less the unit of measurement. Same way if we are to measure linear dimesnion in the form of small arc it would be difficult to put on paer though we can conceptually think of. How can you really compare two angles if they ar not in multiples.

We have limited information to measure things which our brain can conceptualise.

Ahh . . . But if you had a square of uncertain area, say 4/pi, then the inscribed circle would have an exact area of 1.

Bravo....!

Similar to my first post but so much more eloquent!

Do you know the calculus? You can approach an answer if you can define a circumference. Squares are misleading in the first place. No line is possible to define because it is a selection of points in space. The cardinal points of said square are also impossible to define for the same reason. Where do the chosen vectors cross precisely?

Please don't be so sure a square area is so easily determined. There too, the calculus is invaluable but not absolutely determinate.

First of all, WESTERN MATH:::: The system we use around the world is a collection of ideas from all points from the globe. Saying western math is tad amount to saying the earth is not part of the milky way, oh I guess that is also western cosmology. Opps. So, what other math does the non western (sic) world use? The math we use tends to be rather universal.

Now Pi. For your thought process, try using the limit of the inscribed circle as it approaches the first contact point on the square. Then from the limit series, determine the probability of the inscribed circle to exactly overlap one infinitly small point at the exact mid point on the sides of the square.

Or you could just accept that math is not western, eastern, or arctic in structure. But if you have another system please publish this and place it up for review. But, leave the false definitions out of it.

Sorry to say, but the math does not deviate based upon culture, belief (lowest form of knowledge), philosophical view, or religious view.

No. Pi IS a number.

I don't think Pi is a known number. Still we are struggling to make it more accurate.

In any philosophy or logical structure, math included, there has to be some basic assumptions. We assume that there is such a thing as a number line and that pi, though a large repeating decimal, has a real value.

By common understanding, we agree, subject to review, that 3.14 (or however many decimals seems appropriate) is a useful approximation of this number. The significance of the calculation is usually limited by the accuracy of measurement.

i.e. calculate to thousands of decimal places, mark with chalk, cut with axe.

I am also interested in other "directional" mathematics systems. I keep looking for the Easterners but they are hiding behind the sunrise.

Is it possible that it's not western maths which is lacking but perhaps it is too accurate. Maths is a tool which scientists and engineers use to solve problems. Be it real or abstract. We know the value of pi to the god knows what decimal place but this isn't going to make the solution to a problem any more accurate because at the end of the day we will only use a number to the first few decimal places.

When I was studying physics at uni the lecturers would actually take marks off you if you put in too many decimal places.

No, it doesn't bother me, as it is NOT western math. Go back to history books and you will be surprised to learn that is is Arabic math!

Conclusion, no western math is in danger. Hallelujah!

Wangito.

Actually much older than arabic. The arabs were a vessel to convey pre-christian knowledge and eastern knowledge to the modern western world after the dark ages. They had possession of the depositories of knowledge in places such as egypt, and unlike the early roman church, they did not believe that the knowledge was heretical and burnt it.

Actually, I think a papyrus scroll was just uncovered in a sub-Saharan region that, after a team of scientists, decoded it, found Pi inscribed to 14 billion places (the press release is pending). They're still trying to find a way to roll the 50 ton thing back up.

True story!

Hi All,

Have you ever read Shakespeare in German; in my opinion, it's awful.

This is by no means a reflection of the work's "measurement", but rather the "quantitative" nature of its prose; certain English eloquences have no precise counterpart within the German language and vice-versa.

In short, this apparent disparity is attributable to the language used to exact the measurement.

Cheers, Lee.

Just to stir the cauldron a bit - pi IS calculable but we always choose to stop after a few hundred digits. I think no theory depends on extreme accuracy of pi any more than Newton's law of gravitation depends on knowing G to a hundred digits (dG/dt is a different story).

"pi IS calculable but we always choose to stop after a few hundred digits".

Care to prove that?

Which part? I always stop after 5 digits.

I find it refreshing...it points to our native lack of ability to know much about the universe. We simply bumble along on approximations!

Yes, but isn't it all just a question of perspective?

In Euclidian Geometry, a square is a polygon with four sides, in which, a circle may be inscribed. The area of that square may be readily calculated, if the length of the side is known in some number of convenient units. A circle may be readily inscribed inside such a square. Increasing the number of sides allows an increasingly more accurate estimate of the area of the inscribed circle. Such a polygon with an infinite number of sides has an area equal to the area of said inscribed circle, via the calculus, exactly. This is, of course, "duck soup" as the old saying goes.

But, since circular areas are multiples of the radius-squared-times-pi, one could also look at circles being on their own "axis", with units of pi, or 1/pi, as it's unit-of-measure...

I'm not say one should look at it that way. I'm just saying that it could be chosen as one more perspective...

Maybe (western) math is just lacking one more, different, perspective...

Dear Lord, is this still going on? There's no magic in numbers, except for 11.23 and even that is now in question.