secant

2

etsyfindoftheday 3 | 10.19.17

theme thursday: jewelry + hair accessory pairings

all the geometric metallic finds by anethumjewelry

anethumjewelry is based in philadelphia PA, and i’d love to find one of their local stockists next time i visit for work! i could also easily treat myself to one, two, three or more of their geometric metal pieces to add to my everyday look via etsy ;) these are totally mix-n-match and would look awesome throughout the year.

Color

Title: Color 
Summary: In another world, Liam gets to see color.
Characters: Bill Cipher
Rating: K 

A/N: another fic for @cipherpeaks, in exchange for the charity donation. The request was Bill and Liam interacting as adults, in a scenario where he passed the Inspection and was allowed to live. Thanks again for the donation, I hope you like it!
(
Based on Flat Dreams.)

***

When Liam first began working with him at the shop, there were more than a few perplexed - if not downright hostile - glances.

That was to be expected: it is unusual for an Irregular of Liam’s degree to be allowed to live to adulthood, and when it does happen they aren’t usually seen in shops. They usually are given a job as a Government Office clerk of the seventh class, a boring low-paying job, and expected to sleep at the workplace as well. Most families are all right with never seeing them again, the stain gone from their household.

But theirs is not most families, and Bill has better connections than most Triangles do.

Keep reading

En las muchas hojas
Del libro de matemáticas
Un Cociente se enamoró
Un día dolorosamente
De una Incógnita.


La vio con su mirada innumerable
y la vio desde el ápice a la base:
Una figura impar;
ojos de robot, boca de trapecio,
cuerpo rectangular, senos esferoides.


Hizo de la suya una vida
paralela a la de ella,
hasta que se encontraron
en el infinito.


“¿Quién eres tú?” -indagó ella
con ansia radical.
“Pero puedes llamarme hipotenusa”


Y de hablar descubrieron que eran
(lo que en aritmética corresponde a las almas hermanas)
primos entre sí.


Y así se amaron
al cuadrado de la velocidad de la luz,
en una sexta potencia
trazando ,
al sabor del momento
y de la pasión,
rectas, curvas, círculos y líneas sinusoidales
en los jardines de la cuarta dimensión.


Escandalizaron a los ortodoxos de las formas euclidianas
y a los exegetas del Universo infinito.
Rompieron convenciones newtonianas y pitagóricas.


Y en fin resolvieron casarse,
constituir un hogar,
más que un hogar, una perpendicular.
Invitaron como padrinos
al Polígono y a la Bisectriz.
E hicieron planos y ecuaciones y diagramas para el futuro
soñando con una felicidad
integral y diferencial.


Y se casaron y tuvieron una secante y tres conos
muy graciosillos
Y fueron felices
hasta aquel día
en que todo se vuelve al fin
monotonía.


Fue entonces cuando surgió
El Máximo Común Divisor.
Ofreciole, a ella,
una grandeza absoluta
y la redujo a un denominador común.


Él, Cociente, percibió
Que con ella no formaba un todo,
una unidad.
Era un triángulo, llamado amoroso.
De ese problema él era una fracción
la más ordinaria.


Pero fue entonces cuando Einstein descubrió la Relatividad
Y todo lo que era espurio pasó a ser
moralidad
Como en cualquier sociedad.

— 

Millor Fernandes.

2

{5.04.17} Rewriting my notes for the graphs of secant and cosecant

Aside from that, my teachers really love piling tests on the day of my final and/or AP exam. I’m not really worried about them though, and I’m grateful that I’ll learn how to balance my time for when I have a schedule full of APs!

Also OMG the year is almost over!! I can’t believe that, in three years from now, I’ll have made up my mind as to what college/university I will attend and will be finishing my final AP exams… tempus fugit, hey?

Good luck with your AP exams and finals everyone! You’ll make it through this even stronger than you were before, and we all believe in you! For any seniors out there, don’t fall to senioritis! You’re almost done and I’m sure you’ll do great in whatever college you’re going to attend. Your hard work is paying off.

5

All right! So:

I was commissioned to illustrate how a given everywhere-continuous but nowhere-differentiable function fails to be differentiable.

So I made this one up! It’s basically a sum of functions f at the top there.

Anyways you can see at the bottom how when you zoom in on the curve the slope of the secant doesn’t converge and so the function isn’t differentiable (on the right)

Flat World - Utopia

While writing Flat Dreams, there were a lot of scenes and snippes I had in mind that never made it into the fic. A few did as interludes, but most were scrapped. I figured it might be fun to post some as I write them anyway, so here you go. Click here to read all those written so far.
I’ll use Flat World as a title for bits set before Bill got his powers and took over his dimension; Flat Minds for anything set after that.

(Also, I am open to prompts and stuff because why the hell not. So, if you’ve got any, just drop me an ask!)

A/N: I realized that the last few chapters were seriusly depressing, so here’s something more light-hearted. For the most part.
Also the choice of title is entirely @videogamelover99‘s fault.

***

“So, how much is it for this hat?”

“Eighteen secants.”

“Are you serious?”

“Hey, can’t part from that hat for less. I look dashing in it. We had some great moments together.”

The remark caused Nora to roll her eye and turn back to the mirror, adjusting the hat on the upper point right above her eye. It was lovely and she could easily afford it, but half the fun of going there was getting to haggle with Bill about the price. He was a tough one.

“I won’t dare asking for details. How much is it really?”

“Fourteen secants.”

“How much for me?”

“Twenty.”

“You’ve got to be kidding.”

Bill shrugged. “Unlike poor old me, you’re rich. Quit askin’ for discounts.”

Keep reading

anonymous asked:

Hey there! I'm going to be a senior in high school next month, and I'm incredibly interested in pursuing a career in game design. The thing is, while I've been playing around with programming in my down time, my high school doesn't offer any actual computer classes, and I'm worried a lack of preparation might really screw me over when I go to college. Is there any way a student not given opportunities in advanced math and computer classes can study a field like computer science? Thank you!

If your primary focus is on programming, you want to become a good programmer first and become a good game programmer second. I didn’t actually formally learn any computer science until I reached the university level either. I started with the introduction to computer science classes, and worked my way up from there. If you’re going to a university, I wouldn’t worry about not learning it in high school. Just make sure that you have a solid math foundation and understand the concept of proof by induction, and pay attention in your theory and lower division classes once you get to college. School is a place to learn, whether at elementary or university level. Be a good student, go to office hours and talk to the professors and TAs to explain what you don’t understand.

That said, if you are planning on studying computer science for game programming specifically, here’s the list of topics I’ve found to be particularly useful. This is by no means comprehensive, but I have found myself thinking “I’m so glad I learned this in school” more than once about each of these.

  • Algorithms, Big O Notation, and how to calculate your program’s run time
  • Data structures and how to store data. Many times, the solution lies in finding the right structure to solve the problem.
  • Object-oriented principles at work. Object-oriented programming has four fundamental principles - inheritance, encapsulation, dynamic dispatch, and polymorphism. I’ve found myself referring to all four of them quite often.

  • Proof by induction, and just what this means.
  • A rock-solid understanding of trigonometry. How the angle, sine, cosine, tangent, cotangent, secant, and cosecant relate to each other.
  • Matrix math, specifically multiplication and inversion.
  • Vector math. Normalization, addition, and subtraction, especially in 3 dimensions
  • More advanced vector math. How vectors are used to represent planes, and the concepts of the dot and cross product.

It’s ok if you don’t jump into the super advanced subjects right away. Work on building a solid foundation and understanding of these concepts - the more advanced subjects are built on them, and a shaky foundation will lead to confusion when things get advanced.

Concavity and Inflections

Like the first derivative of a function, the second derivative of a function provides useful information about the shape of the graph. It determines whether the graph is bending upward with an increasing slope or downwards with a decreasing slope.

Concavity Definition
If f’’(x) > 0 on interval I, then f is concave up on I.
if f’’(x) < 0 on interval I, then f is concave down on I.

Concavity is defined for only differentiable functions.

Some observations can be made from the graph about concavity.
1. If f is concave up on an interval, then its tangent lines lies below the graph of the function and its secant lines lie above the graph of the function.
2. If f is concave down on an interval, then its tangent lines lies above the graph of the function and its secant lines lie below the graph of the function.
3. If the graph of f has a tangent line at a point, b, and if concavity of f is opposite on opposite sides of that point, then the graph crosses that tangent line at that point, b, changing the concavity of the graph at point b, where b is called the inflection point.

Inflection Points Definition
A point, x₀, is called an inflection point of f if the following is true:
1. The graph of y = f(x) has a tangent line at x₀.
2. The concavity of f is opposite on each side of x₀.

The Second Derivative Test
A function f will have a loc max, or loc min, value at a critical point if its graph is concave downward, or upward, nearby.

If f’(x) = 0, and f’’(x) < 0, then f has a loc max value at x.
If f’(x) = 0, and f’’(x) > 0, then f has a loc min value at x.