Knot theory A knot diagram of the trefoil knot Knots can be described in various ways. Given a method of description, however, there may be more than one description that represents the same knot. For example, a common method of describing a knot is a planar diagram called a knot diagram. Any given knot can be drawn in many different ways using a knot diagram. A complete algorithmic solution to this problem exists, which has unknown complexity. History[edit] Archaeologists have discovered that knot tying dates back to prehistoric times. A mathematical theory of knots was first developed in 1771 by Alexandre-Théophile Vandermonde who explicitly noted the importance of topological features when discussing the properties of knots related to the geometry of position. In the late 1970s, William Thurston introduced hyperbolic geometry into the study of knots with the hyperbolization theorem. Knot equivalence[edit] On the left, the unknot, and a knot equivalent to it. Knot diagrams[edit] or ) + z C(
David Griffiths Emeritus Professor of Physics Knowlton Laboratory of Physics 26 (503) 777-7252 email: griffith@reed.edu Education: Ph. Dissertation: "Covariant Approach to Massless Field Theory in the Radiation Gauge" (advisor: Sidney Coleman) Post-Doctoral positions: 1970-72 University of Utah1972-74 University of Massachusetts, Amherst Employment: 1974 Hampshire College, Amherst, MA1974-77 Mt. Research interests: Classical Electrodynamics Quantum Mechanics Elementary Particle Theory Selected recent student thesis titles: 2009, Robin Bjorkquist, "Hidden Momentum"2008, Jacob Gilman, "A Study of the B+ Meson Decay to ω ρ+"2006, Kevin Connolly, "Quantum Mechanics of the Electric Dipole Potential" 2005, Darren Platt, "Self-Adjoint Extensions and Quantum Mechanics" 2004, Moira Gresham, "Two-Dimensional Radial Laplacian Growth" Selected recent publications: "Quantum Mechanics of the 1/x^2 Potential" (with Andrew Essin), Am. Books: "Introduction to Electrodynamics, 3rd ed Professional activities: Script r: Reed Physics
Digital Drawing Board Creates Objects in Stunning 3D Detail ETOS, or Electronical Tool for Object Sketching, is a tool for designers and architects that lets them see their creations in three dimensions without the need for 3D glasses. The tool uses the familiar shape of a pen and the intuitive function of a touch interface to bring sketches into the real world. The drawing board takes the form of a tablet computer with a built-in stand formed from its folded cover. It displays objects in 3D using lenticular lens technology and motion tracking, which also allows users to move the shapes around with their hands. The pen-shaped input tool performs basic editing functions that are selected by simply turning it along the horizontal or vertical axis.
Teleportation Teleportation is the name given by science fiction writers to the feat of making an object or person disintegrate in one place while a perfect replica appears somewhere else. How this is accomplished is usually not explained in detail, but the general idea seems to be that the original object is scanned in such a way as to extract all the information from it, then this information is transmitted to the receiving location and used to construct the replica, not necessarily from the actual material of the original, but perhaps from atoms of the same kinds, arranged in exactly the same pattern as the original. A teleportation machine would be like a fax machine, except that it would work on 3-dimensional objects as well as documents, it would produce an exact copy rather than an approximate facsimile, and it would destroy the original in the process of scanning it. In 1993 an international group of six scientists, including IBM Fellow Charles H. C.H. Bennett, G. Experimental Articles D.
Eat, Drink and Live Forever: Immortality is 20 Years Away It seems that we’ve been edging toward becoming a race of cyborgs for a number of years. Medical advances like replacement limbs and joints, cochlear implants, and artificial organs are already being used. Improving medical technology and our understanding of anatomy will continue to drive the human race toward immortality, according to scientist Ray Kurzweil. He believes that within 20 years, there will be no need for humans to face death at all. Kurzweil and other scientists believe that by using nanotechnology, we can reprogram our bodies’ “stone-age software” to halt the aging process, then do away with death altogether. In Kurzweil’s perception of the future, we’ll all sport cybernetic limbs and organs, and rely on nanobots to keep us alive through traumatic injuries and illnesses.
Physics Equation Solvers | Blue Solver Appendicitis? Human Appendix Maybe Not Useless After All For a long time, we’ve believed that the human appendix was more or less good for nothing. Darwin postulated that the appendix was a remnant of evolution that was no longer needed. But for the first time, researchers are actually taking a close look at the appendix and its function. And they’ve come to believe that it is, after all, good for something: it may help to restock the stomach with good bacteria after an illness, like a bout of diarrhea. (image via: ashe-villain) Scientists and researchers from Duke University Medical Center, the University of Arizona and Arizona State University collaborated on the study, which concluded that not only is the appendix not useless – it’s also been around far longer than anyone previously thought.
Motion Mountain - The Free Physics Textbook for Download The Elegant Universe: Pt 1 The Elegant Universe: Part 3 PBS Airdate: November 4, 2003 NARRATOR: Now, on NOVA, take a thrill ride into a world stranger than science fiction, where you play the game by breaking some rules, where a new view of the universe pushes you beyond the limits of your wildest imagination. This is the world of "string theory," a way of describing every force and all matter from an atom to earth, to the end of the galaxies—from the birth of time to its final tick, in a single theory, a "Theory of Everything." Our guide to this brave new world is Brian Greene, the bestselling author and physicist. BRIAN GREENE (Columbia University): And no matter how many times I come here, I never seem to get used to it. NARRATOR: Can he help us solve the greatest puzzle of modern physics—that our understanding of the universe is based on two sets of laws that don't agree? NARRATOR: Resolving that contradiction eluded even Einstein, who made it his final quest. S. BRIAN GREENE:The atmosphere was electric. S.
Personal and Historical Perspectives of Hans Bethe