Liessa writes, "PI The Bible. When I was in college, this quote was in one of our first courses on goniometrics (is this the English word?). It's in the book of I Kings 7: 23 and reappears in II Chronicles 4: 2. Yes, I got my Bible out and looked for it."
a) It proves your college education was not wasted.
b) ?'goniometrics' I take it you were studying little garden Gnomes. :wink:
c) Religion arrives in the Riddles forum, and not before time either.
So according to the Bible it's an even 3 (if it was ten cubits across, and thirty cubits around, then this would mean that pi equals three). The Egyptians thought it was 3.16 in 1650 B.C.. Ptolemy figured it was 3.1416 in 150 AD. And on the other side of the world, probably oblivious to Ptolemy's work, Zu Chongzhi calculated it to 355/113. In Bagdad, circa 800 AD, al-KhwarizmiD agreed with Ptolemy; 3.1416 it was, until James Gregory begged to differ in the late 1600s.
Part of the reason why it was so hard to find the true value of Pi (π) was the lack of a good way to precisely measure a circle's circumference when your piece of twine would stretch and deform in the process of taking it. When Archimedes tried, he inscribed two polygons in a circle, one fitting inside and the other outside, so he could calculate the average of their boundaries (he calculated π to be 3.1418). Others found you didn't necessarily need to draw a circle: Georges Buffon found that if you drew a grid of parallel lines, each 1 unit apart, and dropped a pin on it that was also 1 unit in length, then the probability that the pin would fall across a line was 2/π. In 1901, someone dropped a pin 34080 times and got an average of 3.1415929.
Like all these men noticed, everyone everywhere at anytime who's tried to find π have all come up with pretty much the same number, with some more precise than others. It didn't matter if you tried it on the other side of the world, or got your brother to do it, or let the circle relax a bit before trying again, or snuck up on it when it wasn't looking, or waited until mom and dad had gone to bed before creeping down to the study on tiptoe to catch it by surprise, the ratio of a circle's diameter and circumference still was, is, and always will be
3.1415926535897932384626?-and so-on and so-on and so-on...
APPLES
markr:
One - after that it isn't full
Yup, that was my answer...
Yes, he was right again.
Mark:
CLUB
Not I.
Mark sets his own riddle. ?'Not One' , ?'Not Eye' , ?'One eye'.
Let t=1 denote the first week.
For member x, let x(t) denote either "Coffee" or "Tea", whichever member x drinks in week t.
(We are resisting the impulse to joke about drinking weak tea during week t.)
For t>1, define g(x,t) to be twice the number of friends y of x such that
x(t)=y(t-1), plus one if x(t)=x(t-1).
For t>2, define h(x,t) to be twice the number of friends y of x such that
x(t-2)=y(t-1), plus one if x(t-2)=x(t-1).
For t>1, define f(t) to be twice the number of pairs (x,y) of friends such that x(t)=y(t-1) (both (x,y) and (y,x) should be considered), plus the number of members x such that x(t)=x(t-1).
Claim 1: f(t) = sum g(x,t), where the sum runs over members x.
Claim 2: f(t-1) = sum h(x,t), where the sum again runs over x. (This uses the fact that if (x,y) is an edge then (y,x) is an edge.)
Claim 3: g(x,t) is at least as large as h(x,t).
That's because they differ only in the choice of x(t), and x(t) is chosen to make g(x,t) as large as possible, because of the majority vote with the tie-breaker.
Further, g(x,t)=h(x,t) only if x(t)=x(t-2). (If x(t) is different from x(t-2) then exactly one of g(x,t), h(x,t) is even and the other is odd.)
Clearly f(t) is an integer function of t.
Also f(t) is at least as large as f(t-1), with f(t)=f(t-1) only when x(t)=x(t-2) for all x.
Also f(t) is nonnegative, and it is bounded above by 2N(N-1)+N, where N is the number of members.
Wait until f hits its maximum at f(T); then for all t>T+1, we have x(t)=x(t-2). So the club's behavior is periodic with period 1 or 2 after time T.
An example of period 2 is a bipartite graph: the only friendships are between men and women, all men initially drink tea and all women initially drink coffee. Then each week they exchange roles.
Answer 2:
A club with 1000 members that has the friendship graph
1--2--3--4--...--998--999--1000 and starts with the assignment (1,1,0,1,0,1,0,1,...,0,1) (i.e. all even-numbered members, as well as member 1, drink coffee on the first week, and tea for all odd-numbered members except member 1), will run for 998 weeks before settling into an all-coffee regime on the 999th week.
It has been proven impossible to "square the circle." What does it mean to square the circle
multiply a circle by itself
construct a square that perfectly circumscribes a circle
use a straightedge and compass to construct a square equal in area to a given circle
determine the value of pi squared
draw a circle with area equal to pi * (r squared)
A weekend of fun and laughter!
The A two Know Universal H.P. Challenge.
15 questions to be crowned chief Mucklepuklock.
Harry Potter
1. What is the name of the sixth Harry Potter book
2. What is J.K. Rowling's middle name
3. The sixth Harry Potter book will be published on 16th
2005.
4. Who plays Harry Potter in the film series
5. What film certificate did Harry Potter and the Prisoner of Azkaban receive when it was released in the UK
U
PG
12A
15
6. What is the name of the second book in the series
7. What is a 'muggle'
