trigonometry-is-my-bitch:

A  Bézier curve is a mathematically defined curve used in computer graphics and similar applications. The curve is defined by four points: the initial position and the terminating position (which are called “anchors”) and two separate middle points (which are called “handles”). The shape of a Bézier curve can be altered by moving the handles.

The mathematical method for drawing curves was created by Pierre Bézier in the late 1960’s for the manufacturing of automobiles at Renault.

spring-of-mathematics:

Mathematics and Traditional Cuisine

The mathematics of Pasta: A process analysis to find unity, formulas and ways to express structure mathematics of pasta shapes, by their mathematical and geometric properties.
See more at: The Maths of Pasta by George L. Legendre.

Image: 

  • 'Pasta By Design' - Created by a team of designers, ‘Pasta by Design’ book reveals the hidden mathematical beauty of pasta: its geometrical shapes and surfaces are explained by mathematical formulae, drawings and illustrations.
  • Animated gifs - From video: The traditional pasta making techniques used at Della Terra Pasta by Chris Becker [Video] - shared at here.

Types of Pasta in the post (From left to right):  Agnolotti - Tortellini - Saccottini - Sagne Incannulate - Pappardelle.

spring-of-mathematics:

Envelope and String Art

In geometry, an envelope of a family of curves in the plane is a curve that is tangent to each member of the family at some point. Classically, a point on the envelope can be thought of as the intersection of two “adjacent” curves, meaning the limit of intersections of nearby curves. This idea can be generalized to an envelope of surfaces in space, and so on to higher dimensions.

Image:

Reference: Envelope (Mathematics) on Wiki - Envelope on mathworld.wolfram.com.

spring-of-mathematics:

Golden Ratio φ = (1+sqrt(5))/2 = 1.6180339887498948482…
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0. Two quantities a and b are said to be in the golden ratio φ if
(a+b)/a = a/b = φ
One method for finding the value of φ is to start with the left fraction. Through simplifying the fraction and substituting in b/a = 1/φ:
(a+b)/a = 1+ b/a = 1+1/φ
Therefore: 1+1/φ = φ  Multiplying by φ gives: φ^2 - φ - 1 = 0
Using the quadratic formula, two solutions are obtained:: 
φ = (1- sqrt(5))/2 or φ = (1+sqrt(5))/2
Because φ is the ratio between positive quantities φ is necessarily positive:
φ = (1+sqrt(5))/2 = 1.6180339887498948482…
See more at Golden Ratio.
Image: Phi (golden number) by Steve Lewis.

spring-of-mathematics:

Golden Ratio φ = (1+sqrt(5))/2 = 1.6180339887498948482…

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0. Two quantities a and b are said to be in the golden ratio φ if

(a+b)/a = a/b = φ

One method for finding the value of φ is to start with the left fraction. Through simplifying the fraction and substituting in b/a = 1/φ:

(a+b)/a = 1+ b/a = 1+1/φ

Therefore: 1+1/φ = φ 
Multiplying by φ gives: φ^2 - φ - 1 = 0

Using the quadratic formula, two solutions are obtained::

φ = (1- sqrt(5))/2 or φ = (1+sqrt(5))/2

Because φ is the ratio between positive quantities φ is necessarily positive:

φ = (1+sqrt(5))/2 = 1.6180339887498948482…

See more at Golden Ratio.

Image: Phi (golden number) by Steve Lewis.

visualizingmath:

allofthemath:

mathed-potatoes:

When people ask me how I can be a math major and still say I’m not good with numbers, I’m like ‘here, let me draw you a picture.’

All so true.

^For those that are considering majoring in math but are deterred by their lack of number skills, there’s definitely more to mathematics than simply numbers. (I’m not dissing stats or number theory or algebra though. Those are cool too!)

visualizingmath:

allofthemath:

mathed-potatoes:

When people ask me how I can be a math major and still say I’m not good with numbers, I’m like ‘here, let me draw you a picture.’

All so true.

^For those that are considering majoring in math but are deterred by their lack of number skills, there’s definitely more to mathematics than simply numbers. (I’m not dissing stats or number theory or algebra though. Those are cool too!)