http://demonstrations.wolfram.com/TheGrahamClockEscapement
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A clock escapement regulates the progress of the gear train that eventually moves the clock hands. The escapement effectively counts the number of swings made by the pendulum. The escapement in this Demonstration is the Graham dead-beat escapement. The ...
Contributed by: Erik Mahieu
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Views: 5728
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http://demonstrations.wolfram.com/FortescuesTheoremForAThreePhaseUnbalancedSystem
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
In 1918, C. L. Fortescue stated his theorem: N unbalanced phasors can be represented by N systems of N balanced phasors. Sequence components were created to facilitate calculations in unbalanced circuits and systems. Using the theory of symmetrical comp...
Contributed by: Daniel Motter
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Views: 2801
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http://demonstrations.wolfram.com/RotatingAHypercubeIn4D
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
This Demonstration gives a variety of animated rotations of a hypercube in 4D projected to 3D. The axis (set of fixed points) in a 4D rotation is a plane. As a simple example, stop the animation and set all the angles to zero. Drag the first slider; thi...
Contributed by: Gerard Balmens
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Views: 1172
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http://demonstrations.wolfram.com/SandersonEngine
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
The Sanderson engine is based on a highly efficient rocker-arm mechanism to convert reciprocating motion to rotational motion. Each cylinder can have two opposite combustion chambers and the compression ratio can be changed while the engine is running (...
Contributed by: Kay Herbert

Views: 1011
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http://demonstrations.wolfram.com/ARotatingReuleauxTriangle/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A Reuleaux triangle is a curve of constant width formed from an equilateral triangle by joining each pair of vertices with a circular arc centered at the third vertex (each radius is equal to the side length of the triangle). A Reuleaux triangle can be ...
Contributed by: Chris Boucher

Views: 17038
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http://demonstrations.wolfram.com/SimulatingVehicleSuspensionWithASimplifiedQuarterCarModel
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
The simplified quarter-car suspension model is basically a mass-spring-damper system with the car serving as the mass, the suspension coil as the spring, and the shock absorber as the damper. This Demonstration lets you explore the affect of different s...
Contributed by: Erik Mahieu

Views: 18922
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http://demonstrations.wolfram.com/CylindricalCam/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A ball is set into in a skewed groove of a cylinder. When the cylinder rotates, the walls of the groove act as cams and move the ball up and down, which in turn moves a guided bar. This arrangement is a way of producing linear from rotational motion.
Contributed by: Sandor Kabai

Views: 39425
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http://demonstrations.wolfram.com/WankelRotaryEngineEpitrochoidalEnvelopes
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
This Demonstration gives an animation of an epitrochoid and associated planetary-motion envelope curve. The configuration shown has applications in the internal combustion engines invented by Felix Wankel and popularized by Mazda in RX-7 and RX-8 cars. ...
Contributed by: Tony Kelman

Views: 5010
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http://demonstrations.wolfram.com/LamesEllipsoidAndMohrsCirclesPart1/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Starting from the values of the main stresses, this Demonstration displays both the surface (Lame's ellipsoid) made by all the stresses in 3D and the values of the intrinsic components of those stresses, using Mohr's circles.
Contributed by: Luis Martin Yague, Agustin Lacort, and Antxon Sanchez Parandiet
After work by: Eugenio Bravo Sevilla

Views: 6256
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http://demonstrations.wolfram.com/TheMysteryOfTheDisappearingSquare/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Consider the eight orange triangles, four brown pieces, and four squares assembled into the large square shown. By using the slider you can reassemble them into the same large square, but with the middle square missing. Where has it gone?
Contributed by: Jaime Rangel-Mondragon

Views: 28465
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http://demonstrations.wolfram.com/DenavitHartenbergParametersForAThreeLinkRobot
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
The Denavit-Hartenberg (DH) convention for assigning coordinate frames uses four variables to define the reference coordinate frame for each link in a robotic arm. This Demonstration lets you select a three-link combination of revolute (rotating) ...
Contributed by: Aaron T. Becker and Mary Burbage
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Views: 1171
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http://demonstrations.wolfram.com/KinematicsOfARedundantAnthropomorphicArmWithSevenDegreesOfFr
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
The anthropomorphic arm with seven degrees of freedom (DoF) includes redundancy, since the number of joints (n=7) is greater than the dimension of the manipulation variables, which have three position coordinates and three orientation angles (m=6). Alth...
Contributed by: Frederick Wu
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Views: 263
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http://demonstrations.wolfram.com/DupinsIndicatrixOfATorus
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
This Demonstration shows how Dupin's indicatrix changes at a variable point on a torus. In the tangent plane at a point p of a surface M, Dupin's indicatrix is given by the equation ?_1x^2+?_2y^2=1, where the x, y axes coincide with the principal direc...
Contributed by: Sonja Gorjanc and Desana ?tambuk

Views: 1615
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http://demonstrations.wolfram.com/TheParametrizedSzilassiPolyhedron/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
The following steps construct a seven-faced regular toroid, the Szilassi polyhedron.
Contributed by: Lajos Szilassi (University of Szeged, Hungary) and Sandor Kabai

Views: 605
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http://demonstrations.wolfram.com/ImpedanceOfTheRandlesCircuitRedoxReactionEAtARotatingDiskEle
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
This Demonstration plots Faradaic (Z_f) and electrode impedance (Z) for the equivalent circuit (Randles circuit) of the electrochemical redox reaction (E) at a rotating disk electrode (RDE) in the Nyquist and Bode (modulus and phase) planes.
Contributed by: Jean-Paul Diard and Claude Montella

Views: 2850
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http://demonstrations.wolfram.com/ParabolicTroughSolarConcentrator
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Designing a parabolic trough solar concentrator requires specifying: ? the collector aperture, ? the focal length, ? the size of the tube located at focus, ? the degrees out of focus possible before the trough needs to be refocused. This Demonstration w...
Contributed by: Dr. Rolfe A. Leary and Kevin Nimerfro Additional contributions by: Jaebum Jung

Views: 32080
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http://demonstrations.wolfram.com/PartialStandingWaves
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
This Demonstration shows an interactive dynamic plot of the partial standing wave generated by two sinusoids of equal speed and frequency traveling in opposite directions. The forward and backward traveling waves are initialized to have amplitudes 1 and...
Contributed by: Justin Dove

Views: 992
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http://demonstrations.wolfram.com/OldhamCoupling/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A disk with perpendicular grooves on opposite faces is placed between two shafts. Each shaft has a tongue that fits into the grooves of the disk. This arrangement is used in the Oldham coupling for transferring torque between two parallel but noncolline...
Contributed by: Sandor Kabai

Views: 24876
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http://demonstrations.wolfram.com/EquatorialTelescopeMounts/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
To keep an astronomical object within the field of view, telescopes need to be able to compensate for the Earth's rotation. Some telescopes use an equatorial mount, which allows the telescope to track an object along a parallel to the celestial equator....
Contributed by: Jeff Bryant

Views: 6200
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http://demonstrations.wolfram.com/PlotsOfZernikePolynomials
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
This Demonstration shows a 2D contour plot and a choice of 3D plots: a revolution plot, a shadow plot, stereo pairs of the revolution plots, or x and y profiles for various orthonormal Zernike circle polynomials Z_j(?,?). In the 3D plots, you can choose...
Contributed by: James C. Wyant
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Views: 3348
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http://demonstrations.wolfram.com/CompoundOf5Cubes/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
The vertices of the cube 5-compound coincide with those of the dodecahedron. The void inside the five cubes has the shape of a rhombic triacontahedron. The cube 5-compound is one of the stellations of the rhombic triacontahedron.
Contributed by: Sandor Kabai

Views: 656
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http://demonstrations.wolfram.com/ConnectingSkewAxlesWithHyperboloidalGears
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Gears shaped like hyperboloids can be used to build a transmission between skew axles. With a given "skew angle" (the angle between the axles), the eccentricity of two hyperboloids whose axes of symmetry coincide with these axles can be found such that ...
Contributed by: Mark Peterson
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Views: 9622
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http://demonstrations.wolfram.com/ChaoticMotionOfABouncingBallOnAHarmonicallyForcedOscillator
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
This Demonstration shows the map of the movement of a ball bouncing on a harmonically forced oscillator, depending on the frequency, the forcing amplitude, and the coefficient of restitution. The coordinates of each point are given by the dimensionless ...
Contributed by: Soter Gabor
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Views: 180
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http://demonstrations.wolfram.com/TheSixDegreesOfFreedomOfADiatomicMolecule
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
For a diatomic molecule at sufficiently high temperatures, the equipartition of energy theorem distributes an equal portion of the energy, equal to ( 1 ) / ( 2 ) k_BT, among each quadratic term in the Hamiltonian. Here k_B is the Boltzmann constant and ...
Contributed by: Enrique Zeleny

Views: 9088
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http://demonstrations.wolfram.com/MappingLinesAndCirclesOntoTheRiemannSphere
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
One of the great miracles of mathematics is the fact that an infinitely extended plane, which is densely packed with complex numbers, can be mapped onto a sphere with radius ( 1 ) / ( 2 ) and hence an area of ?. Here you can see a decent fraction of the...
Contributed by: Hans-Joachim Domke

Views: 5985
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http://demonstrations.wolfram.com/RealEllipticCurves/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
The intersection of the surface z = x^3 - a y^2 + b x y^2 + c x^2 y with the plane z = A x + B gives an elliptic curve or its degenerate form. The intersection curve is illustrated in real space.
Contributed by: Zubeyir Cinkir

Views: 3182
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http://demonstrations.wolfram.com/AnamorphicPrisms/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Anamorphic prisms are wedge-shaped prism elements that are commonly used to correct the asymmetric beam shape of a laser diode from elliptical to nearly circular in shape. The prisms can expand or contract the beam in one direction without any changes i...
Contributed by: Ann Williamson and Donald Barnhart (Optica Software, a division of iCytTM Mission Technology)

Views: 2520
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http://demonstrations.wolfram.com/ErrorDiffusionDitherPatterns/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
To approximate a gray level on a display with only black or white pixels requires an algorithm which turns pixels on or off to achieve the correct average overall level. Change the kernel or the parameters to see different ways to diffuse the "error" ac...
Contributed by: Stephen Wolfram

Views: 2153
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http://demonstrations.wolfram.com/SquareHoleDrillInThreeDimensions/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
One can combine the use of a Reuleaux triangle to make a square-hole drill with an Oldham coupling to make a drill that has one end following pure circular motion, while the other end has a cutting tool that follows an exact square. This idea appeared i...
Contributed by: Stan Wagon (Macalester College)

Views: 72778
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http://demonstrations.wolfram.com/RotatingBeamFatigueTester
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
This Demonstration plots the tension variation at the surface of a cylindrical specimen in a rotating beam fatigue test. The fatigue life of a material is commonly tested by applying a cyclical load to it, alternating between tension and compression. Fo...
Contributed by: Erik Mahieu
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Views: 2442
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http://demonstrations.wolfram.com/BuildAFrustum
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
This Demonstration lets you set the height and the upper and lower radii of a frustum and shows a diagram of the material you would have to cut to cover the lateral curved part of the frustum. All measurements are in mm.
Contributed by: Nick James
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Views: 2860
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http://demonstrations.wolfram.com/ThrowAHammer/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Throw a hammer and observe how it rotates around its center of gravity as it flies along a parabolic trajectory. A cylindrical target is shown as a visual aid, which can be used for target practice as well.
Contributed by: Sandor Kabai

Views: 1346
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http://demonstrations.wolfram.com/PlayingWithTheHenonMapStartingWithACircleOrASquare
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
This Demonstration shows iterates of the dissipative Henon map [1?4], (x_n+1,y_n+1)=(1+b y_n-a x_n^2,x_n), where a and b are real, acting on 500 equally spaced initial points (x_0,y_0) on a circle or a square. You can drag the crosshairs-shaped locator ...
Contributed by: Ki-Jung Moon
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Views: 375
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http://demonstrations.wolfram.com/OffsetSliderCrankMechanism
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A slider-crank mechanism can be used to convert rotary motion into linear motion or vice-versa. In this Demonstration, the constant angular speed of a crank is converted into the variable linear speed of a sliding block, forced to stay on a straight lin...
Contributed by: Erik Mahieu
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Views: 6054
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http://demonstrations.wolfram.com/TitchenerIllusion/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
The orange circles are exactly the same size. This illusion is due to the psychologist Edward Bradford Titchener. If two circles are surrounded by other circles, the one with larger surrounding circles will appear smaller.
Contributed by: Michael Schreiber

Views: 3671
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http://demonstrations.wolfram.com/ParabolicProjectileMotionShootingAHarmlessTranquilizerDartAt/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A veterinarian (who oddly enough looks like Robin Hood) points a harmless tranquilizer dart directly at a monkey hanging from a branch. The monkey, using its incredible spider-monkey sense, realizes what is going on, and drops from the branch at the exa...
Contributed by: Roberto Castilla-Melendez, Roxana Ramirez-Herrera, and Jose Luis Gomez-Munoz

Views: 7498
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http://demonstrations.wolfram.com/11bConstructATriangleGivenTheLengthsOfTwoSidesAndTheBisector
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
This Demonstration shows an alternative construction of a triangle ABC given the lengths of the sides b and c and the length s of the angle bisector of ?BAC. Construction Draw the line segment DB_1 with interior point A_1 so that ?DA_1?=b and ?A_1B_2?=c...
Contributed by: Izidor Hafner
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Views: 30
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http://demonstrations.wolfram.com/BeadOnARotatingWire/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A bead on a rotating wire is a classic problem in the physics subfield of classical dynamics. A circular wire hoop rotates at a constant angular velocity while a bead, constrained to move only on the wire hoop, moves under the influence of gravity. The ...
Contributed by: Ryan K. Smith (Wolfram Research)

Views: 8943
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http://demonstrations.wolfram.com/LineJaggednessVisualizationWithTheMandelbrotWeierstrassFunct/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
This Demonstration helps visualize the effect of resolution and the apparent fractal dimension on the jaggedness of an irregular line.
Contributed by: Mark D. Normand and Micha Peleg

Views: 1231
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http://demonstrations.wolfram.com/HobermanSphereOctahedron/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Expandable flat rings made of scissors are placed on a sphere's great circles that lie along the edges of an invisible octahedron. The number of scissors in a ring must be divisible by four. The geometry of this assembly corresponds to that of a Hoberma...
Contributed by: Sandor Kabai

Views: 4137
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http://demonstrations.wolfram.com/TamariAttractor
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
The Tamari attractor (from the economist Ben Tamari) is a three-dimensional attractor that models the economic situation of a country.
Contributed by: Enrique Zeleny
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Views: 624
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http://demonstrations.wolfram.com/PolyaVectorFieldsAndComplexIntegrationAlongClosedCurves/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
The Polya vector field for a complex-valued function u(x, y) + i v(x, y) is the vector field ltu(x, y), - v(x, y)gt. This field is displayed along a curve, allowing for a visual interpretation of the complex integral. ...
Contributed by: Don Krug and Steven Wilkinson

Views: 1054
wolframmathematica

http://demonstrations.wolfram.com/MoirePatternsAndCommensurabilityInRotatedGrapheneBilayers
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
This Demonstration shows the appearance of Moire patterns in hexagonal lattice systems as you rotate a honeycomb layer on top of another identical layer by an angle ?. The rotation angle ? can be freely chosen or, as done in this Demonstration, specifie...
Contributed by: Jessica Alfonsi
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Views: 1129
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http://demonstrations.wolfram.com/ThreePyramidsThatFormACube
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Drag the slider to form a cube from the three pyramids.
Contributed by: Karl Scherer
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Views: 3947
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http://demonstrations.wolfram.com/Sphericon
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
A sphericon is approximated using triangular segments. A bicone can be produced if half of the sphericon is rotated by 90 degrees. Notice that an octahedron is obtained if the number of segments is four, and a saddle surface can be created by manipulati...
Contributed by: Sandor Kabai
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Views: 419
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http://demonstrations.wolfram.com/BreakthroughCurvesForAdsorptionWithLongitudinalDiffusionAssu/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
An important unit operation in biotechnology and chemical engineering is fixed-bed adsorption.
Contributed by: Housam Binous

Views: 3323
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http://demonstrations.wolfram.com/FromQuaternionTo3DRotation
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
Any nonzero quaternion ? has a corresponding unitary (length one) quaternion in the same direction as ?. Unitary quaternions are an elegant and efficient way to formalize 3D rotations.
Contributed by: Isabelle Cattiaux-Huillard and Gudrun Albrecht
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Views: 15622
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http://demonstrations.wolfram.com/ConstructingARegularHeptagonUsingLillsMethod
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
This Demonstration shows how to construct a regular heptagon using Lill's method for solving cubic equations. The points of a regular heptagon with vertices on a circle of radius 1 are given by z^7=1. Since z=1 is a solution, if we divide the polynomial...
Contributed by: Izidor Hafner
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Views: 126
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http://demonstrations.wolfram.com/PentagonTilings/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
In 1918, K. Reinhardt discovered five different families of convex pentagons that could tile the plane (1-5). This was the complete list until 1968, when Richard Kershner wrote about three more families of tiling pentagons (6-8). Martin Gardner wrote ab...
Contributed by: Ed Pegg Jr

Views: 1863
wolframmathematica

http://demonstrations.wolfram.com/InstantlyPeriodicGeneralContinuedFractionRepresentationsOfSq/
The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily.
This Demonstration provides a way to instantly write a periodic general continued fraction representation of square roots. This can be used as a quick way to easily approximate the numerical value of square roots.
Contributed by: Michael Morrison

Views: 3091
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