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Videos uploaded by user “wolframmathematica”
The Graham Clock Escapement
 
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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 Audio created with WolframTones: http://tones.wolfram.com
Views: 5728 wolframmathematica
Fortescue's Theorem for a Three-Phase Unbalanced System
 
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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 Audio created with WolframTones: http://tones.wolfram.com
Views: 2801 wolframmathematica
Rotating a Hypercube in 4D
 
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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 Audio created with WolframTones: http://tones.wolfram.com
Views: 1172 wolframmathematica
Sanderson Engine
 
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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 wolframmathematica
A Rotating Reuleaux Triangle
 
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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 wolframmathematica
Simulating Vehicle Suspension with a Simplified Quarter-Car Model
 
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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 wolframmathematica
Cylindrical Cam
 
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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 wolframmathematica
Wankel Rotary Engine: Epitrochoidal Envelopes
 
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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 wolframmathematica
Lame's Ellipsoid and Mohr's Circles (Part 1)
 
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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 wolframmathematica
The Mystery of the Disappearing Square
 
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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 wolframmathematica
Denavit-Hartenberg Parameters for a Three-Link Robot
 
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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 Audio created with WolframTones: http://tones.wolfram.com
Views: 1171 wolframmathematica
Kinematics of a Redundant Anthropomorphic Arm with Seven Degrees of Freedom
 
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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 Audio created with WolframTones: http://tones.wolfram.com
Views: 263 wolframmathematica
Dupin's Indicatrix of a Torus
 
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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 wolframmathematica
The Parametrized Szilassi Polyhedron
 
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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 wolframmathematica
Impedance of the Randles Circuit: Redox Reaction (E) at a Rotating Disk Electrode (RDE)
 
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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 wolframmathematica
Parabolic Trough Solar Concentrator
 
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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 wolframmathematica
Partial Standing Waves
 
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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 wolframmathematica
Oldham Coupling
 
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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 wolframmathematica
Equatorial Telescope Mounts
 
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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 wolframmathematica
Plots of Zernike Polynomials
 
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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 Audio created with WolframTones: http://tones.wolfram.com
Views: 3348 wolframmathematica
Compound of 5 Cubes
 
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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 wolframmathematica
Connecting Skew Axles with Hyperboloidal Gears
 
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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 Audio created with WolframTones: http://tones.wolfram.com
Views: 9622 wolframmathematica
Chaotic Motion of a Bouncing Ball on a Harmonically Forced Oscillator
 
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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 Audio created with WolframTones: http://tones.wolfram.com
Views: 180 wolframmathematica
The Six Degrees of Freedom of a Diatomic Molecule
 
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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 wolframmathematica
Mapping Lines and Circles onto the Riemann Sphere
 
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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 wolframmathematica
Real Elliptic Curves
 
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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 wolframmathematica
Anamorphic Prisms
 
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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 wolframmathematica
Error-Diffusion Dither Patterns
 
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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 wolframmathematica
Square-Hole Drill in Three Dimensions
 
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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 wolframmathematica
Rotating Beam Fatigue Tester
 
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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 Audio created with WolframTones: http://tones.wolfram.com
Views: 2442 wolframmathematica
Build a Frustum
 
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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 Audio created with WolframTones: http://tones.wolfram.com
Views: 2860 wolframmathematica
Throw a Hammer
 
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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 wolframmathematica
Playing with the Henon Map Starting with a Circle or a Square
 
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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 Audio created with WolframTones: http://tones.wolfram.com
Views: 375 wolframmathematica
Offset Slider-Crank Mechanism
 
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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 Audio created with WolframTones: http://tones.wolfram.com
Views: 6054 wolframmathematica
Titchener Illusion
 
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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 wolframmathematica
Parabolic Projectile Motion: Shooting a Harmless Tranquilizer Dart at a Falling Monkey
 
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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 wolframmathematica
11b. Construct a Triangle Given the Lengths of Two Sides and the Bisector of Their Common Angle
 
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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 Audio created with WolframTones: http://tones.wolfram.com
Views: 30 wolframmathematica
Bead on a Rotating Wire
 
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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 wolframmathematica
Line Jaggedness Visualization with the Mandelbrot-Weierstrass Function
 
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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 wolframmathematica
Hoberman Sphere (Octahedron)
 
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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 wolframmathematica
Tamari Attractor
 
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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 Audio created with WolframTones: http://tones.wolfram.com
Views: 624 wolframmathematica
Polya Vector Fields and Complex Integration along Closed Curves
 
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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
Moire Patterns and Commensurability in Rotated Graphene Bilayers
 
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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 Audio created with WolframTones: http://tones.wolfram.com
Views: 1129 wolframmathematica
Three Pyramids That Form a Cube
 
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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 Audio created with WolframTones: http://tones.wolfram.com
Views: 3947 wolframmathematica
Sphericon
 
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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 Audio created with WolframTones: http://tones.wolfram.com
Views: 419 wolframmathematica
Breakthrough Curves for Adsorption with Longitudinal Diffusion Assuming Linear Equilibrium
 
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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 wolframmathematica
From Quaternion to 3D Rotation
 
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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 Audio created with WolframTones: http://tones.wolfram.com
Views: 15622 wolframmathematica
Constructing a Regular Heptagon Using Lill's Method
 
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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 Audio created with WolframTones: http://tones.wolfram.com
Views: 126 wolframmathematica
Pentagon Tilings
 
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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
Instantly Periodic General Continued Fraction Representations of Square Roots
 
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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 wolframmathematica