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Pyritohedron, version 1.0, 2018-01-15 Rolf PÃ¼tter The pyritohedron is a dodecahedron with twelve congruent pentagonal faces, which are not necessarily regular. Its name stems from the crystal pyrite. It comes in a whole family of polyhedra parametrized by h, 0<=h<=1. For h=0, you get the cube, for h=0.62, the regular dodecahedron, and for h=1 the rhombic dodecahedron.
This program implements the Hungarian algorithm: Given a positive mxn -Matrix, find an assignment of rows to columns (each row and column may be used at most once) such that the sum of matrix elements is minimal.
The rhombic dodecahedron can be constructed by attaching a square pyramid to each of the six faces of a cube. Choose the hight of these pyramids to be one half of the cube's edge length. Pairs of adjacent triangular faces from neighboring pyramids then add to form the twelve rhombic faces.
The user enters a directed weighted graph with a source and a sink (a flow network). The program then computes a maximal flow and a minimal cut.
This programs simulates a single waiting line at a bank teller. The user can enter then mean interarrival time between two customers and the mean service time.
The user's task is to fill a regular hexagon completely with little calissons (=rhombi) of three different types.
The user enters n vertices of a polygon without self-intersection. It is the floor plan of an art gallery. The user's task is then to pick at most [n/3] (the square brackets simbolise the floor function) vertices where to place guards so that they cover the whole interior of the gallery. It is understood that the guards may look in any direction they choose and that their view is blocked only by the walls.
This program uses Lindenmayer systems to draw fractals and plants.
The program displays the RÃ¶ssler attractor and the Lorenz attractor.
|ifs.zip||6k||17-01-21||Iterated function systems|
The program uses iterated function systems and the chaos game to create fractals. The user can define and display his own ifs.
The user enters up to five points in the Euclidean plane. The program then constructs an associated minimal Steiner tree.
|curveshortening.zip||16k||16-12-16||Curve Shortening Flow|
The user enters a closed curve c. The program then moves each point of c in the inwards normal direction with a speed proportional to the signed curvature at that point.
The user enters up to 52 points, "nodes", in the Euclidean plane. The program then connects these points by a function graph (x,y(x)) (press [Enter] or [blank]), where y(x) is a natural spline, or by a curve (x(t),y(t)), where x(t) and y(t) are natural splines (press [.]), or by a closed curve (x(t),y(t)) composed of periodic splines, press [,].
The Hilbert curve is a continuous mapping c:[0,1]->[0,1]x[0,1] from the unit interval into the unit square whose image is the whole square. It is the limit for n->infinity of curves cn which consist of horzontal and vertical line segments. The program draws these curves up to n=7 (n=8 for a computer screen).
A small wheel (circle) c of radius r moves tangentially without slipping along the inside or outside of a fixed larger circle C with radius R>r. A point A is fixed to c with distance d to the center of c. As c rolls along C, A describes a curve which mathematicians call a hypotrochoid (if c moves inside C) or epitrochoid (if c moves outside C).
|trammelofarchimedes.zip||5k||16-05-29||Trammel of Archimedes|
The trammel of Archimedes is a tool that draws the shape of an ellipse. Two points, A and B, are fixed to a rod by pivots which are confined to move on the x-axis and the y-axis respectively. Any point C fixed to the rod will now describe an ellipse or a circle as A and B move along their axes.
The program shows the motion of a Reuleaux triangle in the square with edge length equal to the triangle's width.
The user enters a set S of points in the Euclidean plane. For each s in S, the Voronoi region of s is the set of points in the plane closer to s than to any other point of S. The program draws the Voronoi regions of the entered points and the corresponding Delaunay triangulation.
The user enters up to 52 points ("cities") in the Euclidean plane. The salesman's task is to find the shortest closed tour touching each city exacty once.
|netsofacube.zip||6k||16-03-29||Nets of a cube|
Press numbers 1 to 6 to place colors or numbers into the square grid. Press [Enter]. If the filled squares form the net of a cube, this cube is shown on the right side of the screen. You can rotate it via the arrow keys.
The user enters the functional term x(n) of a sequence of real numbers, for example x(n)=n^1.5. The program then constructs the following sequence of plane points: (u,v)(0)=(0,0), (u,v)(n)=(u,v)(n-1)+s*(cos(2*pi*x(n)),sin(2*pi*x(n))) and draws the line segment between consecutive points. A number of curious curves arises.
A latin square of order n is an nxn-matrix of n different symbols (e.g. numbers, letters or colors) in which each symbol occurs exactly once in each row and each column. Let S and T be two sets of n symbols each. A graeco-latin square of order n over S and T then is a matrix M of ordered pairs (s,t) in SxT, in which each pair occurs exactly once and which decomposes into two latin squares if s and t are considered separately. For n=2 and n=6, no graeco-latin squares exist. The program displays graeco-latin squares up to order 10.
The program demonstrates the fact that every positive integer can be written as a sum of four squares of integers (Lagrange's theorem). The user enters the number and the decomposition is shown.
A Ulam spiral is a rectangular grid of natural numbers in the plane, starting at the origin and spiraling out counterclockwise in growing squares. If only primes are marked, straight lines parallel to the main diagonals become visible.
The user enters the initial position and direction of a ball on an elliptic billiard table. The program then traces the path of the ball starting in the given direction. You can also try to hit a second ball going via the border.
|jordan.zip||14k||15-09-29||Jordan Normal Form|
The user enters a quadratic real matrix A up to size 5x5. The program then computes the characteristic polynomial. It also determines the real Jordan normal form J of A and the associated transition matrix S with S^-1*A*S=J
The user enters the term of a function f(x,y). The program then draws the wire frame of the graph of f and up to 15 level lines.
The program shows the intersection of a torus with the xy-plane. The torus can be moved parallelly to the z-axis and rotated about its three axes.
The user's task is to cut the unit square into four polygons and then to form a triangle by rotating and translating the parts. A special choice of parameters yields an equilateral triangle.
|minimumspanningtree.zip||7k||15-06-14||Minimum Spanning Tree|
The user can construct a graph by entering vertices and edges. The task is then to find the Euclidean minimum spanning tree, that is, a graph without cycles that connects all the vertices and has minimal total length. The Enter key gives a program-generated solution.
The program offers an infinity of proofs for the Pythagorean theorem. It allows the user to cut the two smaller squares into different polygons and to rearrange then into the square over the hypotenuse.
Plot bode diagrams right on your calculator
The program demonstrates the fact that the hyperbolic plane can be tiled by regular polygons with n vertices for each n>=3. It uses the Poincaré model (the unit) disc to do this. In this model, orthocircles (circles that intersect the unit circle orthogonally) take the role of straight lines.
This program visualizes several complex functions by drawing the image of four different grids under these functions.
|crosscut.zip||8k||15-02-12||Cut the Cross|
It's a popular game to divide a square with a few straight cuts and to form new shapes from the produced polygons. This program works the other way round. With the help of a moving square grid, the user effects at most four cuts on a swiss cross. His task is then to reassemble the pieces to a square.
This program offers a guessing game the user can play against the calculator. The user fills three baskets with up to ten balls in four different colors. The calculator then chooses a basket at random. The user's task is to guess which. As evidence the calculator draws balls (with replacement) from the chosen basket and discloses their color and number. With the help of Bayes' formula, a new probability is ascribed to each basket. The user can now guess the number of the chosen basket or order another draw until the probabilties become more clear.
The program constructs a conic section through five given points. The user can move the point marked by a circle with the arrow keys and watch how the conic section changes. The coefficients of the corresponding equation can be displayed.
A Hamiltionian path on a graph is a path that visits each vertex exactly once. A Hamiltonian cycle is a closed Hamiltonian path. The program allows the user to define a graph on the screen. He can then proceed to construct a Hamiltonian path or cycle on this graph if possible. He can get hints from the program.
The user enters points on the screen which are connected by straight lines. Hitting the Enter key then closes the polygon. The right arrow key now constructs a new polygon consisting of the midpoints of the edges of the old one. If the number of vertices is odd, this process is mathematically invertible. This is actuated by the left arrow key.
Plot bode Diagrams instantly on your calculator! Define transfer functiona and this programm plots the gain and phase diagrams for you.
|sd2.2.zip||101k||13-11-27||SD2: step by step derivatives in natural display|
Does determine the derivative of a function, step by step and in natural display. Requires OS 3.2 or later.
|mathgame.zip||41k||12-10-25||Math Practice Game|
This game gives you 15 seconds to complete 4 random math problems as fast as possible
This is based off a TI84 program to help you memorize pi, e, root2, and phi. You can try memorizing up to 1000 digits. In addition, the next four digits are given when you mess up.
|baseconverternspire.zip||14k||12-04-05||Base Converter Nspire|
This program will convert your numbers in between different bases up to base 36! Made with Nspire Lua, for OS >3.0
TabVar is the most advanced function study program for the Nspire! It features a graphical variation table and 10+ programs to perform different operations on functions, such as extensively studying a function, finding the domain of definition, getting the equation of a tangent, making an integration by parts, checking the parity or periodicity of a function, comparing two functions... A full french and english documentation is included, and all programs adapt their language to your calculator's setting.
Represent 8 polyhedra in 3D! Choose the color, the rendering mode, the zoom... You also can draw 3D functions. The 3D drawing is really fast.
ISOBoard is an isometric dot paper sheet for you TI NSpire. Just put the script in your documents, and add seamless dot paper drawings to your math projects!