2. age-of-awakening:


    Fibonacci you crazy bastard….

    As seen in the solar system (by no ridiculous coincidence), Venus orbits the Sun 8 times in the same period that Earth orbits the sun 13 times! Drawing a line between Earth & Venus every week results in a spectacular FIVE side symmetry!!

    Lets bring up those Fibonacci numbers again: 1, 1, 2, 3, 5, 8, 13, 21, 34..

    So if we imagine planets with Fibonacci orbits, do they create Fibonacci symmetries?!

    You bet!! Depicted here is a:

    • 2 sided symmetry (5 orbits x 3 orbits)
    • 3 sided symmetry (8 orbits x 5 orbits)
    • sided symmetry (13 orbits x 8 orbits) - like Earth & Venus
    • sided symmetry (21 orbits x 13 orbits)

    I wonder if relationships like this exist somewhere in the universe….

    Read the Book    |    Follow

    finallyyyyyy i get to see a motion version of this<3

    (via theworkingtools)

  3. spring-of-mathematics:

    Reconsidering time: Linear Cycle Clock & Spiral of Theodorus in Mathematics:

    Linear Cycle Clock & Ideas: Exploring the concept of time continues to fascinate designers. Like Uji by Fabrica, the Linear Cycle from BCXSY is not a common clock. Instead of the usual rotating dials, the clock features a revolving element that shows the passing of time on a linear plate instead of a circular one - Source: Commissioned by Isabelle Daëron and Fabien Petiot for Roues Libres (Freewheel) for D’Days 2014 in Paris, this unique time display offers an alternative to the ordinary clock and makes us consider how we advance through time.

    Spiral of Theodorus & Construction: In geometry, the spiral of Theodorus (also called square root spiral, Einstein spiral or Pythagorean spiral) is a spiral composed of contiguous right triangles. It was first constructed by Theodorus of Cyrene.
    The spiral is started with an isosceles right triangle, with each leg having unit length. Another right triangle is formed, an automedian right triangle with one leg being the hypotenuse of the prior triangle (with length √2) and the other leg having length of 1; the length of the hypotenuse of this second triangle is √3. The process then repeats; the i th triangle in the sequence is a right triangle with side lengths √i and 1, and with hypotenuse √i + 1. For example, the 16th triangle has sides measuring 4 (=√16), 1 and hypotenuse of √17.

    Images: Spiral of Theodorus on Wikipedia & The article: Spiral of Theodorus by Elizabeth Nelli on Jwilson.coe.uga.edu.

    (via ljiljana147)

  4. trippiest:


    Now I can die in peace.

    Trippiest blog on Tumblr!

    (via ziindo)

  5. (Source: wookmark.com)

  6. (Source: mythirdeye.info)

  9. Whale song art

    These exquisite images are the visual
    representations of songs sung by whales and
    dolphins. The sounds were recorded by US
    engineer Mark Fischer and transformed into
    visuals by clever mathematics. But these are
    not just pretty pictures - the patterns reveal
    tantalising clues to how these majestic
    animals communicate through song.


    (Source: sciencephoto.com)

  10. musical harmonics

    (Source: aton432hz.info)

  11. Music and Harmonics Theory - 432 HZ - Sacred Musical Scales

    (Source: keychests.com)

  12. Figs. 27–38. Outermost part of mature staminate flower in Figs. 27–30 and intermediate part in Figs. 31–34. Phyllotactic variation in staminate flowers. Numbers in figures follow the initiation sequence of primordia (SEM micrographs). 27. Flower with trimerous-like configuration. 28. Flower with tetramerous-like configuration. 29. Irregular phyllotaxy. 30. Irregular configuration. Three stamens extraordinarily expanded. 31, 32. Trimerous-like configuration, but size of each stamen differs. 33, 34. Tetramerous-like configurations, but symmetry differs. 35–37. Innermost part of three flowers with successive spiral initiation. 38. Innermost part of mature staminate flower with Fibonacci spiral configuration. Scale bars = 500 μm (Figs. 27–30), 50 μm (Figs. 31–38)

    (Source: amjbot.org)

  13. mathhombre:


    Type of Spirals: A spiral is a curve in the plane or in the space, which runs around a centre in a special way.
    Different spirals follow. Most of them are produced by formulas:The radius r(t) and the angle t are proportional for the simplest spiral, the spiral of Archimedes. Therefore the equation is:
    (3) Polar equation: r(t) = at [a is constant].
    From this follows
    (2) Parameter form:  x(t) = at cos(t), y(t) = at sin(t),
    (1) Central equation:  x²+y² = a²[arc tan (y/x)]².

    You can make a  spiral by two motions of a point: There is a uniform motion in a fixed direction and a motion in a circle with constant speed. Both motions start at the same point. 
    (1) The uniform motion on the left moves a point to the right. - There are nine snapshots.
    (2) The motion with a constant angular velocity moves the point on a spiral at the same time. - There is a point every 8th turn.
    (3) A spiral as a curve comes, if you draw the point at every turn(Image).

    Figure 1: (1) Archimedean spiral - (2) Equiangular Spiral (Logarithmic Spiral, Bernoulli’s Spiral).
    Figure 2 : (1) Clothoide (Cornu Spiral) - (2) Golden spiral (Fibonacci number).

    More Spirals: If you replace the term r(t)=at of the Archimedean spiral by other terms, you get a number of new spirals. There are six spirals, which you can describe with the functions f(x)=x^a [a=2,1/2,-1/2,-1] and  f(x)=exp(x), f(x)=ln(x). You distinguish two groups depending on how the parameter t grows from 0.

    Figure 4:  If the absolute modulus of a function r(t) is increasing, the spirals run from inside to outside and go above all limits. The spiral 1 is called parabolic spiral or Fermat’s spiral.
    Figure 5: If the absolute modulus of a function r(t) is decreasing, the spirals run from outside to inside. They generally run to the centre, but they don’t reach it. There is a pole.  Spiral 2 is called the Lituus (crooked staff).

    Figure 7: Spirals Made of Line Segments.

    Source:  Spirals by Jürgen Köller.

    See more on Wikipedia:  SpiralArchimedean spiralCornu spiralFermat’s spiralHyperbolic spiralLituus, Logarithmic spiral
    Fibonacci spiral, Golden spiral, Rhumb line, Ulam spiral
    Hermann Heights Monument, Hermannsdenkmal.

    Image: I shared at Spirals by Jürgen Köller - Ferns by Margaret Oomen & Ferns by Rocky.

    Spiral compulsion. But this is a handy reference.

    (via organicalchemist)


    1) The icosahedron Platonic solid; 2) a chlorophyll protein from a pea ; 3) Circogonia icosahedra radiolaria (a single cell organism living in water); 4) also a radilarian organism; 5) the AIDS virus; 6) ancient roman dice; 7) a drawing of a hyperbolic icosahedron.


    (Source: delisiart.com)

  15. bigblueboo:

    moire mandala