Pi is not 22/7!
(by “The Cyberiad” by Stanislaw Lem)
Come, let us hasten to a higher plane,
Where dyads tread the fairy fields of Venn,
Their indices bedecked from one to n,
Commingled in an endless Markov chain!
Come, every frustum longs to be a cone,
And every vector dreams of matrices.
Hark to the gentle gradient of the breeze:
It whispers of a more ergodic zone.
In Riemann, Hilbert or in Banach space
Let superscripts and subscripts go their ways.
Our asymptotes no longer out of phase,
We shall encounter, counting, face to face.
I’ll grant thee random access to my heart,
Thou’lt tell me all the constants of thy love;
And so we two shall all love’s lemmas prove,
And in our bound partition never part.
For what did Cauchy know, or Christoffel,
Or Fourier, or any Boole or Euler,
Wielding their compasses, their pens and rulers,
Of thy supernal sinusoidal spell?
Cancel me not–for what then shall remain?
Abscissas, some mantissas, modules, modes,
A root or two, a torus and a node:
The inverse of my verse, a null domain.
Eclipse of bliss, converge, O lips divine!
The product of our scalars is defined!
Cyberiad draws nigh, and the skew mind
Cuts capers like a happy haversine.
I see the eigenvalue in thy eye,
I hear the tender tensor in thy sigh.
Bernoulli would have been content to die,
Had he but known such a2 cos 2ϕ!
A math professor has a problem with his plumbing, so he hires a
plumber. He watches the plumber use a wrench to tighten a joint, then
is handed a bill for a couple hundred dollars. “I had no idea that
plumbers made this much money!” he said, “I’ve been a math professor
for 20 years and I can’t claim to make this much per hour.”
So the professor decides to become a plumber and for a while he’s very
happy. Then the licensing board decides that plumbers need to know more
math, and the professor, along with all the other plumbers, have to
attend a math class. The teacher called on him one day to go to the
board and compute the circumference of a circle. The professor gets to
the board, but for some reason, he can’t remember the formula to
determine the circumference. So he decides to derive the formula.
The professor fills the board with calculations, but at the end he gets
a formula that he knows is incorrect. Figuring he made a mistake
somewhere along the line, he erases all his calculations and starts
again, but again he gets the same incorrect answer. He’s stumped! He
stares at the blackboard and tries to figure out what he’s doing wrong.
Then, in unison, all the other plumbers say, “Switch the limits on your integral!”
If you choose an answer to this question at random what is the chance you will be correct?
(discussion at the Math Subreddit)
One study by researchers looks at how starting a bit later in the morning can improve the performance by students. The study’s lead author is a pediatrician at Hasbro Children’s Hospital in Providence, and concludes that:
“Giving teens 30 extra minutes to start their school day leads to
more alertness in class, better moods, less tardiness, and even
Another (different) study links IQ to sleep schedule. They find that night owls are smarter than other people.
Bedtimes and wake-up times for Americans in their 20s by IQ:
Very Dull (IQ < 75)
Weekday: 11:41 P.M.-7:20 A.M.
Weekend: 12:35 A.M.-10:09 A.M.
Normal (90 < IQ < 110)
Weekday: 12:10 A.M.-7:32 A.M.
Weekend: 1:13 A.M.-10:14 A.M.
Very Bright (IQ > 125)
Weekday: 12:29 A.M.-7:52 A.M.
Weekend: 1:44 A.M.-11:07 A.M.
They claim that:
“The modern world contains many features our slow-to-evolve brains still find unfamiliar–cars, TVs, hot dogs on a stick. But the world has always thrown new stuff at us, and brighter humans may adapt more ably.”
Richard over at Tales of the Golem; or, the Modern Epimetheus claims to have “convincing experimental disproof of Pythagoras’s theorem!”
In the first picture, the water covers the area a^2+b^2 while in the third picture, it covers an area larger than that of c^2. Thus, a^2+b^2 > c^2. Guess all of mathematics was wrong!