Dimensions: A Walk Through Mathematics A film for a wide audience! Nine chapters, two hours of maths, that take you gradually up to the fourth dimension. Mathematical vertigo guaranteed! Dimension Two - Hipparchus shows us how to describe the position of any point on Earth with two numbers... and explains the stereographic projection: how to draw a map of the world. Dimension Three - M.C. Escher talks about the adventures of two-dimensional creatures trying to imagine what three-dimensional objects look like. The Fourth Dimension - Mathematician Ludwig Schläfli talks about objects that live in the fourth dimension... and shows a parade of four-dimensional polytopes, strange objects with 24, 120 and even 600 faces! Complex Numbers - Mathematician Adrien Douady explains complex numbers. Fibration - Mathematician Heinz Hopf explains his "fibration". Proof - Mathematician Bernhard Riemann explains the importance of proofs in mathematics. Watch the full documentary now (playlist - )
Tree of Life Return to "Download Files" Page You are welcome to download the following graphic image of the Tree of Life for non-commercial, educational purposes: Tree of Life (~3,000 species, based on rRNA sequences) (pdf, 368 KB) (see Science, 2003, 300:1692-1697) This file can be printed as a wall poster. Printing at least 54" wide is recommended. Tree of Life tattoo, courtesy of Clare D'Alberto, who is working on her Ph.D. in biology at the University of Melbourne. The organisms depicted in this tattoo are (starting at 4 o'clock and going around clockwise): (1) a cyanobacterium (Anabaena); (2) a radiolarian (Acantharea); (3) a dinoflagellate (Ceratium); (4) an angiosperm (Spider Orchid); (5) a couple species of fungi (Penicillium and a yeast); (6) a ctenophore (comb jelly); (7) a mollusc (nudibranch); (8) an echinoderm (brittle star); and (9) a vertebrate (Weedy Sea Dragon). Here is another great Tree of Life tattoo! Cover of Molecular Systmatics, 2nd ed
Dimension (mathematics and physics) A diagram showing the first four spatial dimensions. 1-D: Two points A and B can be connected to a line, giving a new line segment AB. 2-D: Two parallel line segments AB and CD can be connected to become a square, with the corners marked as ABCD. 3-D: Two parallel squares ABCD and EFGH can be connected to become a cube, with the corners marked as ABCDEFGH. 4-D: Two parallel cubes ABCDEFGH and IJKLMNOP can be connected to become a hypercube, with the corners marked as ABCDEFGHIJKLMNOP. In physical terms, dimension refers to the constituent structure of all space (cf. volume) and its position in time (perceived as a scalar dimension along the t-axis), as well as the spatial constitution of objects within—structures that correlate with both particle and field conceptions, interact according to relative properties of mass—and are fundamentally mathematical in description. The concept of dimension is not restricted to physical objects. A tesseract is an example of a four-dimensional object.
The 2011 Nobel Prize in Physics - Press Release 4 October 2011 The Royal Swedish Academy of Sciences has decided to award the Nobel Prize in Physics for 2011 with one half to Saul Perlmutter The Supernova Cosmology Project Lawrence Berkeley National Laboratory and University of California, Berkeley, CA, USA and the other half jointly to Brian P. and Adam G. "for the discovery of the accelerating expansion of the Universe through observations of distant supernovae" Written in the stars "Some say the world will end in fire, some say in ice..." * What will be the final destiny of the Universe? In 1998, cosmology was shaken at its foundations as two research teams presented their findings. The research teams raced to map the Universe by locating the most distant supernovae. The teams used a particular kind of supernova, called type Ia supernova. For almost a century, the Universe has been known to be expanding as a consequence of the Big Bang about 14 billion years ago. Saul Perlmutter, U.S. citizen. Brian P. Adam G. Recommended:
Golden spiral Approximate and true golden spirals: the green spiral is made from quarter-circles tangent to the interior of each square, while the red spiral is a golden spiral, a special type of logarithmic spiral. Overlapping portions appear yellow. The length of the side of a larger square to the next smaller square is in the golden ratio. In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio.[1] That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes. Formula[edit] The polar equation for a golden spiral is the same as for other logarithmic spirals, but with a special value of the growth factor b:[2] or with e being the base of Natural Logarithms, a being an arbitrary positive real constant, and b such that when θ is a right angle (a quarter turn in either direction): Therefore, b is given by The numerical value of b depends on whether the right angle is measured as 90 degrees or as for θ in degrees;
sleepyti.me bedtime calculator Logarithmic spiral Self-similar growth curve A logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic spiral was Albrecht Dürer (1525) who called it an "eternal line" ("ewige Linie").[1][2] More than a century later, the curve was discussed by Descartes (1638), and later extensively investigated by Jacob Bernoulli, who called it Spira mirabilis, "the marvelous spiral". The logarithmic spiral can be distinguished from the Archimedean spiral by the fact that the distances between the turnings of a logarithmic spiral increase in geometric progression, while in an Archimedean spiral these distances are constant. In polar coordinates the logarithmic spiral can be written as[3] or with being the base of natural logarithms, and being real constants. In Cartesian coordinates [edit] The logarithmic spiral with the polar equation can be represented in Cartesian coordinates by In the complex plane Spira mirabilis and Jacob Bernoulli
Magic mushrooms’ effects illuminated in brain imaging studies Brain scans of people taking psilocybin have given scientists the most detailed picture to date of how psychedelic drugs work. Brain scans of people under the influence of the psilocybin, the active ingredient in magic mushrooms, have given scientists the most detailed picture to date of how psychedelic drugs work. The findings of two studies being published in scientific journals this week identify areas of the brain where activity is suppressed by psilocybin and suggest that it helps people to experience memories more vividly. In the first study, published today in Proceedings of the National Academy of Sciences (PNAS), 30 healthy volunteers had psilocybin infused into their blood while inside magnetic resonance imaging (MRI) scanners, which measure changes in brain activity. The scans showed that activity decreased in "hub" regions of the brain - areas that are especially well-connected with other areas. R Carhart-Harris et al. R Carhart-Harris et al.
Convex regular polychoron In mathematics, a regular 4-polytope is a regular four-dimensional polytope. They are the four-dimensional analogs of the regular polyhedra in three dimensions and the regular polygons in two dimensions. Regular 4-polytopes were first described by the Swiss mathematician Ludwig Schläfli in the mid-19th century, although the full set were not discovered until later. There are six convex and ten star regular 4-polytopes, giving a total of sixteen. History[edit] The tesseract is one of 6 convex regular 4-polytopes The convex 4-polytopes were first described by the Swiss mathematician Ludwig Schläfli in the mid-19th century. Schläfli also found four of the regular star 4-polytopes; (the grand 120-cell, great stellated 120-cell, grand 600-cell, and great grand stellated 120-cell). Construction[edit] The existence of a regular 4-polytope is constrained by the existence of the regular polyhedra which form its cells and a dihedral angle constraint Regular convex 4-polytopes[edit] Properties[edit] Note: