Artist Nike Savvas transforms mathematic formulas into beautiful sculptures.
Artist Owen Schuh’s beautiful math
Schuh on his work:
My work seeks to illuminate the entwining relations between embodied mind, mathematics, and the physical world. My artwork is structured by mathematical functions, which though relatively simple in nature yield outcomes of surprising organic complexity. I have created this work by hand using, at most, the aid of a pocket calculator.
This is the Frankenstein aspect of mathematics — we have the authority to define our creations, to instill in them whatever features or properties we choose, but we have no say in what behaviors may then ensue as a consequence of our choices.
Paul Lockhart — Exultation
I just love the way he envisions the world of math, how vivid he portrays the behavior of the notions and numbers and their abilities once you’ve given them a certain value. Numbers have lives of their own. We can’t control them, once we decide what we mean by them, we have no say in how they behave. Nothing we can do except watch them and try to understand them. If they taught public educational math in this way, I think I would have been a lot more interested in the subject to be quite honest.
If you account for the mass of the three quarks inside of the proton — then you’ve only accounted for 10% of the proton’s mass.
Though the rest is “empty space” and has no “particles” in it — it’s actually a boiling, bubbling brew of “virtual particles”, that pop in and out of existence in time-scales so short they can’t be measured.
This image is from an animation based on a mathematical model of what that other 90% looks like. These fields of “potential existence” [in constant flux] generate the lion’s share of the mass we observe in the proton.
Meaning: Your potential is roughly 90% — compared to your actual, which is only 10%.
Nautilus II Table by Marc Fish
That’s an extreme-a-hedron.
This is a form of a Johnson solid, a shape where every face is a polygon, but not necessarily the same polygon.
derivatives of Gaussian PDF’s
The Candle Problem
Given a book of matches, a box of thumbtacks, and a candle, how can you fix the candle to the wall so that its wax won’t drip onto the table below?
See Answer Below
Pin the box to the wall, put the candle in the box, and light it.
In experiments, Gestalt psychologist Karl Duncker found that most subjects instead tried to pin the candle directly to the wall or to use melted wax to affix it there (neither worked). Duncker called this “functional fixedness” — a “mental block against using an object in a new way that is required to solve a problem.” In this case, subjects had “fixated” on the box’s function as a container, which prevented them from considering it as a platform. If the box was empty at the start of the experiment, they were more likely to find the correct solution.
In a 2000 study, psychologists Tim German and Margaret Defeyter found the 6- and 7-year-olds show signs of functional fixedness, but 5-year-olds appear immune to it: “Rather than taking into account only the properfunction of an object, they adopt and agents-goals view of function in which any intentional use of an object can be its function.”
the mathematical paradox of extra dimensional space.
I’d say “he’s a kid and didn’t add it up” but he got that notion from a grown-up.
Also, you know, two wars and the economy falling apart and shit. Dubya was terrible, and it’s adorable that a 15-year-old thinks Yahoo Answers is going to prove otherwise. -Jess
Because prime numbers are indivisible (except by 1 and themselves), and because all other numbers can be written as multiples of them, they are often regarded as the “atoms” of the math world. Despite their importance, the distribution of prime numbers among the integers is still a mystery. There is no pattern dictating which numbers will be prime or how far apart successive primes will be. The seeming randomness of the primes makes the pattern found in “Ulam spirals” very strange indeed. In 1963, the mathematician Stanislaw Ulam noticed an odd pattern while doodling in his notebook during a presentation: When integers are written in a spiral, prime numbers always seem to fall along diagonal lines. This in itself wasn’t so surprising, because all prime numbers except for the number 2 are odd, and diagonal lines in integer spirals are alternately odd and even. Much more startling was the tendency of prime numbers to lie on some diagonals more than others — and this happens regardless of whether you start with 1 in the middle, or any other number. Even when you zoom out to a much larger scale, as in the plot of hundreds of numbers below, you can see clear diagonal lines of primes (black dots), with some lines stronger than others. There are mathematical conjectures as to why this prime pattern emerges, but nothing has been proven.
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