The Elegant Universe: Pt 1 The Elegant Universe: Part 3 PBS Airdate: November 4, 2003 NARRATOR: Now, on NOVA, take a thrill ride into a world stranger than science fiction, where you play the game by breaking some rules, where a new view of the universe pushes you beyond the limits of your wildest imagination. BRIAN GREENE (Columbia University): And no matter how many times I come here, I never seem to get used to it. NARRATOR: Can he help us solve the greatest puzzle of modern physics—that our understanding of the universe is based on two sets of laws that don't agree? NARRATOR: Resolving that contradiction eluded even Einstein, who made it his final quest. BRIAN GREENE: We really may live in a universe with more dimensions than meet the eye. AMANDA PEET (University of Toronto): People who have said that there were extra dimensions of space have been labeled crackpots, or people who are bananas. NARRATOR: A mirage of science and mathematics or the ultimate theory of everything? S. We see 400 employees in three years.
Weierstrass functions Weierstrass functions are famous for being continuous everywhere, but differentiable "nowhere". Here is an example of one: It is not hard to show that this series converges for all x. Here's a graph of the function. You can see it's pretty bumpy. Below is an animation, zooming into the graph at x=1. Wikipedia and MathWorld both have informative entries on Weierstrass functions. back to Dr.
gimme some oven Personal and Historical Perspectives of Hans Bethe 6174 (number) 6174 is known as Kaprekar's constant[1][2][3] after the Indian mathematician D. R. Kaprekar. This number is notable for the following property: Take any four-digit number, using at least two different digits. 9990 – 0999 = 8991 (rather than 999 – 999 = 0) 9831 reaches 6174 after 7 iterations: 8820 – 0288 = 8532 (rather than 882 – 288 = 594) 8774, 8477, 8747, 7748, 7487, 7847, 7784, 4877, 4787, and 4778 reach 6174 after 4 iterations: Note that in each iteration of Kaprekar's routine, the two numbers being subtracted one from the other have the same digit sum and hence the same remainder modulo 9. Sequence of Kaprekar transformations ending in 6174 Sequence of three digit Kaprekar transformations ending in 495 Kaprekar number Bowley, Rover. "6174 is Kaprekar's Constant".
Joe Pastry Motion Mountain - The Free Physics Textbook for Download Collatz conjecture The Collatz conjecture is a conjecture in mathematics named after Lothar Collatz, who first proposed it in 1937. The conjecture is also known as the 3n + 1 conjecture, the Ulam conjecture (after Stanisław Ulam), Kakutani's problem (after Shizuo Kakutani), the Thwaites conjecture (after Sir Bryan Thwaites), Hasse's algorithm (after Helmut Hasse), or the Syracuse problem;[1][2] the sequence of numbers involved is referred to as the hailstone sequence or hailstone numbers (because the values are usually subject to multiple descents and ascents like hailstones in a cloud),[3][4] or as wondrous numbers.[5] Take any natural number n. Paul Erdős said about the Collatz conjecture: "Mathematics may not be ready for such problems In 1972, J. Statement of the problem[edit] Histogram of stopping times for the numbers 1 to 100 million. Numbers from 1 to 9999 and their corresponding total stopping time. Consider the following operation on an arbitrary positive integer: In notation: (that is: applied to
The Brownie That Will Change Your Life Let me start off by saying that viewer discretion is advised for today’s post. OK now with the story that preludes possibly the greatest brownie I have ever sunk my teeth in thus far in my life. Last Saturday Mrs. Zesty had a baby shower to attend and she was designated for a dessert/sweet treat for the girls. Last week was a bit of a zoo and I think I forgot about prepping this dessert until Friday afternoon at work. After work I did a quick scan for some ideas and came up with a chocolate caramel brownie. I knew time was tight and I didn’t want to spend all night Friday night to prep a dessert. This recipe, I cannot take any credit for and nor will I try as it is compliments of Nestle Toll House and as you can see from the reviews…. Ingredients 1 pkg. (18.25 oz.) chocolate cake mix1 cup chopped nuts ( Optional )1 cup Evaporated Milk1/2 cup (1 stick) butter or margarine, melted35 (10-oz. pkg.) caramels, unwrapped2 cups (12-oz. pkg.) Method Thanks zesty
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