fuckyeahmath:

ilovecharts:

via poorlymade

fuckyeahmath:

karlobenson:

Experimenting with Hypocycloids (Diversion VI)

I fascinated and treated myself with the simple trigonometric functions that I was working with previously just to relieve my stress after having finished a rigorous monthly data summary and report back from work. I never knew someone from Browny-knows-where reminded me of the very entertaining spirograph! Yes, a spirograph - it comprises a set of small, plastic-made wheels of different sizes and two large rings with teeth on their inside as well as outside rims which anyone can basically use to draw families of hypocycloids and epicycloids. The toy was introduced in the western culture in 1970’s; and, though I live in a third world country, I was fortunate enough to have a grasp on this wonderfully educational graphing toy - I quite remember my elementary public school library had me borrow a set one time. 

In this photo, I constructed hypocycloids by using the same smoothed-line XY-scatter plots easily available from Excel. The equations are easy and how selfish would I be if I don’t post them here?!

OK, here they are:

x(Ɵ) = r(k-1)cosƟ + rcos((k-1)Ɵ); and

y(Ɵ) = r(k-1)sinƟ - rsin((k-1)Ɵ).

I decided r to be equivalent to 1 just for ease of encoding and let k be any number (it’s actually the ratio between the radius of the bigger wheel against the smaller one). For the case of my Diversion VI photo, I simply selected the values 7.2, 4, 2.1, and 6.

Now, I’m off to the market to find myself one of those spirographs. Excel must make the plotting easy, but the real toy offers more.

fuckyeahmath:

dear-lover:

variation 64 of 70 of the pentagonal hexecontahedron

Tim Keller (via azspot)

It’s a shame that more people of faith don’t allow the “[discard] after long reflection” advice to apply to their beliefs, not just their doubts.

(via danielholter)

a4rizm:

La souffrance soulage la culpabilité, aussi la douleur qui apporte la vie dans le monde est-elle inconsciemment doublement enviable pour l’homme.

Joan Riviere et Melanie Kein, L’amour et la haine, Payot, 2001, Paris, Traduit de l’anglais par Annette Stronck, Titre Original : Love, Hate and Reparation, P.58.

fuckyeahmath:

In mathematics, an algebraic number is a complex number that is a root of a non-zero polynomial in one variable with rational (or equivalently, integer) coefficients.

Pictured above: Algebraic numbers colored by degree.

fuckyeahmath:

cafcaf:

Sphere of Chords (by Michæl Paukner)

Via fuckyeahmath

La première étude de l’homme qui veut être poète est sa propre connaissance, entière; il cherche son âme, il l’inspecte, Il la tente, I’apprend. Dès qu’il la sait, il doit la cultiver; cela semble simple: en tout cerveau s’accomplit un développement naturel; tant d’égoistes se proclament auteurs; il en est bien d’autres qui s’attribuent leur progrès intellectuel! - Mais il s’agit de faire l’âme monstrueuse: à l’instar des comprachicos, quoi! Imaginez un homme s’implantant et se cultivant des verrues sur le visage.

Je dis qu’il faut être voyant, se faire voyant.

Le Poète se fait voyant par un long, immense et raisonné dérèglement de tous les sens. Toutes les formes d’amour, de souffrance, de folie; il cherche lui-même, il épuise en lui tous les poisons, pour n’en garder que les quintessences. Ineffable torture où il a besoin de toute la foi, de toute la force surhumaine, où il devient entre tous le grand malade, le grand criminel, le grand maudit, - et le suprême Savant! - Car il arrive à l’inconnu! Puisqu’il a cultivé son âme, déjà riche, plus qu’aucun! Il arrive à l’inconnu, et quand, affolé, il finirait par perdre l’intelligence de ses visions, il les a vues! Qu’il crève dans son bondissement par les choses inouïes et innombrables: viendront d’autres horribles travailleurs; ils commenceront par les horizons où l’autre s’est affaissé!

Translation:

The first task of the man who wants to be a poet is to study his own awareness of himself, in its entirety; he seeks out his soul, he inspects it, he tests it, he learns it. As soon as he knows it, he must cultivate it!… —But the problem is to make the soul into a monster, like the compachicos, you know? Think of a man grafting warts onto his face and growing them there.

I say you have to be a visionary, make yourself a visionary.

A Poet makes himself a visionary through a long, boundless, and systematized disorganization of all the senses. All forms of love, of suffering, of madness; he searches himself, he exhausts within himself all poisons and preserves their quintessence’s. Unspeakable torment, where he will need the greatest faith, a superhuman strength, where he becomes among all men the great invalid, the great criminal, the great accursed—and the Supreme Scientist!

— Les lettres du voyant (The Letters of the Seer), Rimbaud