Science, Art and Photography

archiemcphee:

This stunning installation of 888,246 red ceramic poppies was created by ceramic artist Paul Cummins and stage designer Tom Piper in commemoration of the centennial of Britain’s involvement in World War I. Entitled Blood Swept Lands and Seas of Red, each flower represents a British or Colonial military fatality.

This staggering installation is a work in progress, with the ceramic pippies being planted by volunteers in the dry moat that surrounds the Tower of London. The planting process began a few weeks ago and will continue throughout the summer until a final flower is symbolically planted on November 11, 2014.

Visit the Historic Royal Palaces website to learn more about this moving project. You can also follow the progress of the volunteer planters by following the #TowerPoppies on Twitter.

[via Colossal]

wasbella102:

Kerry Anne Sullivan: The Patchwork of Man

wasbella102:

Kerry Anne Sullivan: The Patchwork of Man

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

(via the-science-of-time)