Ellipse, stuck at origin, rotates

jpedmaths:

Take ellipse:

apply rotation to variables:

to make new equations:

then vary

 to get rotating ellipse:

image

note that addition of an image term only to the original equation, under certain limitations of coefficients, means a rotation only.

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ozandros:

Hurray! I made a tiny TMNT gif inspired by the newest movie :D

ozandros:

Hurray! I made a tiny TMNT gif inspired by the newest movie :D

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prostheticknowledge:

Division by Zero

Latest sound art installation by vtol is a levitating speaker that plays generated glitch noises - video embedded below:

autonomous, zero gravity sound object
- magnetic levitation coil/magnet system
- bluetooth sound receiver
- 2 channel micro sound system
- pure data for glitch sounds

Link

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sixpenceee:

Informal infographic depicting evolution 

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beesandbombs:

globe

beesandbombs:

globe

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fer1972:

Nature and Noise: Photography by Anna Marinenko

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Dry Your Tears, Áfrika. John Williams - (Amistad)

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becausebirds:

An amethyst in bird-form, meet the Costa’s Hummingbird. A desert hummingbird, Costa’s Hummingbird breeds in the Sonoran and Mojave Deserts of California and Arizona.

becausebirds:

An amethyst in bird-form, meet the Costa’s Hummingbird. A desert hummingbird, Costa’s Hummingbird breeds in the Sonoran and Mojave Deserts of California and Arizona.

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spring-of-mathematics:

Herwig Hauser Classic(P2) - Authors | Herwig Hauser

Nepali: Let us look at the defining equation (xy−z3−1)= (1−x2−y2)of Nepali. The symmetry between x and y is enforced by the quadratic polynomial x2+y2, which is rotation symmetrical in contrast to the monomial xy. Sections with horizontal planes z = c yield closed curves being almost circles. The simultaneous occurrence of squares and third powers produces the tapering at the top.The lateral boundary curve of Nepali is not an exact circle but is arching up and down like the brim of a hat. Its projection to the horizontal xy plane, however, is a circle as can be seen from the top view. The surface shown is bounded; hence there was no need to limit the view by sphere intersection. This fact can be directly derived from the formula by accurate analysis.

Zeck (Tick): The simple Tick equation x2+y2 = z3(1−z) fully dictates the geometry just as with the other surfaces; that means, both the singular points and the outer shape, the curvature and the extension are clearly defined by the four monomials x2, y2, −z3 und z4. As a result, the formula is a very efficient way to codify forms which appear complicated. However, the geometric information cannot always be read from the formula. The local shape of the surface near a given point can be explicitly defined, in most cases; the techniques of local analytic geometry have a good effect. Defining the global structure requires much more efforts and cannot always be satisfactorily accomplished.

Kreisel(Spinning Top): To illustrate the shape of a spinning top as a solution set of a simple algebraic equation needs some inventive mathematics! It is, indeed, not clear mathematically, at first sight, what this equation must look like because different equations can provide similar looking forms. The image shows the equation 60(x2+y2)z= (60−x2−y2−z2)3. The rotation symmetry round the vertical z axis is identified by x and y occurring in the quadratic polynomial x2+y2. The third power on the right hand side is necessary to produce the two points. And as z occurs only in even powers, the surface is symmetrical with respect to the reflection in the horizontal xy plane. The parameter 60 in the equation is used for aesthetic reasons.

 Eistüte (Cone):  The horizontal section through Cone is a so-called rosette curve: A small wheel rolls round the interior of an annular body while a pencil fixed to the wheel is drawing a curve (like a Spirograph).  Different curves are formed depending on the ratio of the two radii. The curve closes if the ratio is a rational number.  In our case it is the four- leaf clover. Our cone has the advantage that four scoops of ice-cream will fit in!

Helix: The Lemniscate is the plane curve with the equation y4+z2 = y2. It results from the circle y2+z2 =1 by substituting z by z/y. Geometrically, the substitution corresponds to a distortion of the circle to a figure of eight loop. If y4+z2 = y2 is conceived as equation with three variables x, y and z (where x is hidden) then the solution set is a surface in the three-dimensional space, i. e. the cylinder above the lemniscate. The Helix equation y4+x2z2 = y2 is yielded by substituting z by xz. From the geometrical view, this construction is a kind of folding. The symmetry with respect to x and z is clearly visible. For the final formula we added the factors 2 and 6 to slightly stretch Helix. The singular locus is a crossing of straight lines. The sections of Helix with the planes x = c or z = c are lemniscates for c ≠ 0, whereas the sections y = c are hyperbola pairs.

Himmel & Hölle (Heaven and Hell): A piece of paper is folded and is held from beneath such that you can put your four fingers in the four corners so formed. By spreading your fingers the figure opens in two different ways so that two of the four inner sides can be seen at a time.

This figure reminds us of the popular children’s fortune teller game where you have to predict which colour will show up – blue for heaven and red for hell (hence the name!)

By adding up the squares at y and z you get the highest exponent 4. This is called an equation of the 4th degree. The higher the degree the more complicated it is to calculate the surface.

See more at: http://imaginary.org/gallery/herwig-hauser-classic

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myartexperiments:

Code
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becojo:


Rainbow trefoil knot

becojo:

Rainbow trefoil knot

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Reblog if you are

spiderfish21:

shaxaphone:

s4rcoline:

image

I can’t believe I watched that whole thing. Smh. That’s how I know I am.

where are the notes

The notes are bored.

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plasmatics-life:

Mini Rainbow | (by Ben Owen)

plasmatics-life:

Mini Rainbow | (by Ben Owen)

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