Module, Proportion, Symmetry, and Rhythm . . . . Architecture of Crystals . . . . Patterns of Growth . . . . Modularity of Knowing . . . . Review of Proportion . . . . Duality and Synthesis in the Music of Béla Bartók . . . . The Essence of Rhythm . . . . The Modular Principle and Biological Form . . . . The Unit and the Whole
Principles of Relationship:
The Elements of Drawing [John Ruskin]
Measure - National Institute of Standards & Technology - Virtual Museum
Dynamics - Factors Contributing to Forces in a Composition
The Geometry Center [Center for Computation and Visualization of Geometric Structure, the Univ. of Minnesota Science and Technology Center]
The Golden Ratio
Harmony and Proportion - John Boyd-Brent, M.A. (Royal College of Art)
The Crop Circular - "Crop circles and their relationship to Euclidean Geometry and Diatonic Ratios."
Exploratorium Online Exhibits, including: Depth Spinner, Changing Illusions, Fading Dot, Droodles, Sliding Gray Step, Shimmer, Trapezoidal Window - Requires Shockwave
Atom in a Box, The Atomic Orbitals [September 9, 1998] - "One of the great advances in human knowledge of the twentieth century is the birth of the theory of Quantum mechanics. It has lead to some of the most common technologies used today, including the little transistors that make up the computers you're using to read this. One of the mysteries it revealed was the structure of the atom. Quantum mechanics describes that the electron (and all of the universe for that matter) exists in any of a multitude of states. The particular physical situation determines what and how many states there are. Borrowing from some of the techniques in mathematics, physicists organize these states into a particular set of mathematically convenient states called "eigenstates". Eigenstates are good to use because what makes one eigenstate different from another usually has a physical meaning. They also can make an horribly difficult problem managable. These orbitals' physical structure describe effects from how atoms bond to form compounds, magnetism, the size of atoms, the structure of crystals, to the structure of matter that we see around us."
Probability & Statistics [The Chance Database]
A New Mathematical Mystery - "Math is really about the human mind, about how people can think effectively, and why curiosity is quite a good guide," explaining that curiosity is tied in some way with intuition. "You don't see what you're seeing until you see it," Dr. Thurston said, "but when you do see it, it lets you see many other things." Depending on who is talking, Poincaré's conjecture can sound either daunting or deceptively simple. It asserts that if any loop in a certain kind of three-dimensional space can be shrunk to a point without ripping or tearing either the loop or the space, the space is equivalent to a sphere. The conjecture is fundamental to topology, the branch of math that deals with shapes, sometimes described as geometry without the details. . . . " - (NYtimes - 8/15/2006) - Transcribed here
ExploreELearning - Math and other science tools. "An interactive learning experience - Points in the plane; Linear equations; Systems; Inequalities; Exponentials; Complex numbers; Absolute value; Reflections; Probability."
Your Sky - "The interactive planetarium of the Web. You can produce maps in the forms described for any time and date, viewpoint, and observing location. If you enter the orbital elements of an asteroid or comet, Your Sky will compute its current position and plot it on the map. Each map is accompanied by an ephemeris for the Sun, Moon, planets, and any tracked asteroid or comet. A control panel permits customisation of which objects are plotted, limiting magnitudes, colour scheme, image size, and other parameters; each control is linked to its description in the help file. Your Sky provides three ways to view the sky with links, where appropriate, among the various presentations."
Land, Sea, Air and The Scale of the Universe
'Physics, Astronomy, & Mathematics'
A B C D E F G H I J K L M N
O P Q R S T U V W X Y Z
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