The area of a circle...

[ckissick]

Originally Posted by jyl

Suppose radius r = sqrt ( X / pi ) where X is any rational number. Then area is X = pi * r^2 and is, almost definitionally, a rational number.

Let's say r=10/sqrt(pi)

Then r= 10/1.7724...
r=5.6418...

Then A=pi*5.6418...^2

Or, A=100.0000000...

So, there are an infinite number of circles with an area that is a rational number. And an infinite number of circles with an area that is an irrational number. Whoa, that's weird.

[Bill Verburg]

Originally Posted by Amail

...
I remember a paradox about an arrow fired at a target. Before the shot it is distance D from the target. At some point, it will be D/2 from the target. At another point, it is (D/2)/2 from the target. You can continue to cut the remaining distance in half, but you never get to the target. Of course, unless you're me, you will hit the target, so you get past this never ending sequence of halves. Maybe the circle is the same thing - you can't put a real number on it, but you sure as heck can cut a stick to that length.

That's one of Zeno's 9 paradoxes, the solution is to know calculus where the sum of an infinite series can be shown to be finite despite what logic may say about it.

[Bill Verburg]

Originally Posted by sammyg2

3.141592653589793238462643383279502884197169399375 10582097494459230781640628620899862803482534211706 79821480865132823066470938446095505822317253594081 28481117450284102701938521105559644622948954930381 96442881097566593344612847564823378678316527120190 91456485669234603486104543266482133936072602491412 73724587006606315588174881520920962829254091715364 36789259036001133053054882046652138414695194151160 94330572703657595919530921861173819326117931051185 48074462379962749567351885752724891227938183011949 12983367336244065664308602139494639522473719070217 98609437027705392171762931767523846748184676694051 32000568127145263560827785771342757789609173637178 72146844090122495343014654958537105079227968925892 35420199561121290219608640344181598136297747713099 60518707211349999998372978049951059731732816096318 59502445945534690830264252230825334468503526193118 81710100031378387528865875332083814206171776691473 03598253490428755468731159562863882353787593751957 78185778053217122680661300192787661119590921642019 89380952572010654858632788659361533818279682303019 52035301852968995773622599413891249721775283479131 51557485724245415069595082953311686172785588907509 83817546374649393192550604009277016711390098488240 12858361603563707660104710181942955596198946767837 44944825537977472684710404753464620804668425906949 12933136770289891521047521620569660240580381501935 11253382430035587640247496473263914199272604269922 79678235478163600934172164121992458631503028618297 45557067498385054945885869269956909272107975093029 55321165344987202755960236480665499119881834797753 56636980742654252786255181841757467289097777279380 00816470600161452491921732172147723501414419735685 48161361157352552133475741849468438523323907394143 33454776241686251898356948556209921922218427255025 42568876717904946016534668049886272327917860857843 83827967976681454100953883786360950680064225125205 11739298489608412848862694560424196528502221066118 63067442786220391949450471237137869609563643719172 87467764657573962413890865832645995813390478027590 10

keep going you haven't even begun to scratch the surface of it, the record(to my sometimes faulty memory) goes a Japanese HS math class, they got a super computer printout to 1.3511 trillion places

[James Brown]

pie-r-square? pie-r-round, CAKE-r-square!

[TimT]

Yes

I remember a paradox about an arrow fired at a target. Before the shot it is distance D from the target. At some point, it will be D/2 from the target. At another point, it is (D/2)/2 from the target. You can continue to cut the remaining distance in half, but you never get to the target.

again yes

by definition all rational #s are finite ie they can be expressed as a fraction.

there is no rational # that is not also finite

here's something else to think about, between any 2 rationals #s is an infinite # of irrational #s, the reverse is not true,

Yes.. same is true when measuring something.....

I know it pretty basic calculus... local linearity was something of an eye opener... as x approaches zero.

However x never gets to zero... there are infinite divisions

[DanielDudley]

Of course you can have a finite number as the area. The answer itself would only be approximate, not the reality.

[masraum]

Originally Posted by sammyg2

No WONDER he's a moderator.
Although I'd think a masters in child psychology might be more useful .........

I was on another board today, and on the status where for Bill it says "moderator" for one of the moderators it said "cat herder". I thought that was funny and apt.

[Bill Verburg]

Originally Posted by DanielDudley

Of course you can have a finite number as the area. The answer itself would only be approximate, not the reality.

nope an exact finite, rational area is possible, as is an exact integer answer, the only inexactness is from trying to write pi as a rational #(ie either as a fraction or repeating decimal(1 and all other integers are considered to be repeating because it can be expressed exactly as 1.0000... w/ as many zeros as pleases you))

in fact the definition of a rational # is that which can be written as a fraction or repeating decimal, 1/3 1/2, 5/4, 1, 1, 1000045, 4 1/9 etc all are rational and can be written as a fraction, only irrational and imaginary #s can not be written that way

that's the beauty of math, it's the only place where exact solutions exist.

[RWebb]

we need a math thread...

[flatbutt]

Originally Posted by Icemaster

Bill, you have obviously forgotten more on this than I will ever know.

the five is backerds