Enter a computation above or click on an example below. Arithmetic Algebra Graphing Geometry- Triangle data, side lengths specified: 7, 24, 25 triangle
- Triangle data, vertex coordinates specified: (0,0), (5,3), (3,7) triangle
- Conic Sections gallery: conic section
- Quadric Surfaces gallery: quadric surface
- Galleries of Polyhedra: Platonic solids , Archimedean solids , prisms , antiprisms , Johnson solids
- Properties of a particular polyhedron: cuboctahedron
- Fractals: Koch snowflake , Sierpinski gasket , Sierpinski carpet , Mandelbrot set
- Knot diagrams: trefoil knot , 4_1 knot
Trigonometry Probability Statistics- Calculate basic statistics of a data set: statistics {25, 35, 10, 17, 29, 14, 21, 31}
(includes mean, median, standard deviation... click on "more" for more) - Calculate a curve of best fit (sequence): cubic fit {20.9, 23.2, 26.2, 26.4, 16.3, -12.2, -60.6, -128.9}
- Calculate a curve of best fit (data points): quadratic fit { (1.3, 2.2), (2.1, 5.8), (3.7, 10.2), (4.2, 11.8) }
- Other available curve fits include: linear, quadratic, cubic, quartic, quintic, sextic, exponential, logarithmic, periodic
Logic Sequences and Series Calculus- Limits: lim (sin x)/x as x->0
- Summation Notation: sum j^2, j=1 to 100
- Derivatives: (x^3)'
- Complicated Derivatives, alternate notation: d/dx 4*x*sin(x^2) + e^(tan(x))
Also Try: click on "Show Steps" in the upper-right corner of the W|A window. - Antiderivatives/Indefinite Integrals: integrate x^3
- Definite Integrals: integrate x^3 from 1 to 2
- Improper Integrals: integrate (sin x)/x dx, x=0..infinity
- Taylor Series: taylor series sin x
- Vector Derivatives: d/dt (3t^3, sin(sqrt(t)), t^337)
- Gradient: grad sin(x^2 y)z
- Divergence of a vector field: div (x^3-y^2, 2xy, z)
- Curl of a vector field: curl (x^3-y^2, 2xy, z)
- Fourier Series (function x^3, degree 4 approx.): FourierSeries[x^3, x, 4]
Differential Equations Linear Algebra- Solve system of linear equations: solve 2x + 3y = 4, 3x + 4y = 5, 3x + 5y + z = 6
- 2D vector properties: vector {3, 4}
(graph, length, unit vector, polar coordinates) - 3D vector properties: vector {3, 3, 7}
(graph, length, unit vector, spherical coordinates) - Dot product: {3, 3, 7} dot {1, 2, 3}
- Cross product: {3, 3, 7} cross {1, 2, 3}
- Matrix arithmetic: {{2,-3},{4,5}} . {{1,2},{3,4}} + {{2,-1},{-1,2}}
- Solving matrix equations: solve {{1,2},{-2,3}}.{x,y} = {5,7}
- Matrix arithmetic with parameters: inverse {{a, b}, {c, d}}
- Properties of a square matrix: {{2,3,3},{4,5,4},{1,1,1}}
(dimensions, determinant, trace, characteristic polynomial, inverse, eigenvalues, eigenvectors) - Matrices of Geometric Transformations: rotate 30 degrees , rotate 30 degrees with center (4,3) , reflect across y=x+1
Abstract Algebra- Addition and Multiplication Tables: Z/7Z
Note: using large groups, such as Z/15Z, with result in a graphical display
- Quaternion Group Operation Table: quaternion group
For lots more examples of mathematical computations: http://www.wolframalpha.com/examples/Math.html Also, don't forget that Wolfram|Alpha does more than just math... for example: Adelphi University |
ď Wolfram-Alpha-Examples.pdf (62k) Lee Stemkoski, Jul 28, 2011 11:16 AM
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