visumath
A (growing) collection of educational math visualizations in desmos and geogebra graphing calculators.
Please, rather bookmark this site than the desmos URLs since the latter will change on updates!
Contents
R1
Trigonometric functions
Real valued trigonometric functions, geometric reasoning with help of the unit circle, identities, derivatives and antiderivatives: sin, arcsin, cos, arccos, tan, arctan, cot, arccot, sec, arcsec, csc, arccsc
https://www.desmos.com/calculator/5dms91pmgz
Angle sum identities:
https://www.desmos.com/calculator/qs0vt2ojbh
Angle difference identities:
https://www.desmos.com/calculator/plyunzieof
Hyperbolic functions
Hyperbolic sine, cosine, tangent and the unit hyperbola.
https://www.desmos.com/calculator/bgqxibub4u
ln, e, exp, W
Natural logarithm, Euler number, exponential function and LambertW-function of real values.
https://www.desmos.com/calculator/fknzali1gx
R2
Vector addition
Adding and subtracting vectors.
https://www.desmos.com/calculator/blx95ejvti
Scalar multiplication
Scaling vectors.
https://www.desmos.com/calculator/dnyvphayhr
Inner product
Dot product
https://www.desmos.com/calculator/7kxoinpssq
Homogeneous coordinates
Transformation to and from homogeneous coordinates, normalization and far points.
https://www.desmos.com/calculator/padkgx5uhb
Line equations
Line equation in standard form and derivation of parametric, slope-intercept, Hesse, polar and homogeneous coordinate forms.
https://www.desmos.com/calculator/si4r5rrtkl
Rotation
Rotation of canonical base vectors, coordinates, and line equations.
https://www.desmos.com/calculator/9mxcidhljn
Refraction
Refraction and inner reflection of a ray of light at a plane surface between two homogeneous media.
https://www.desmos.com/calculator/gasu2wvno7
Curvature
Curvature and osculating circle of a continuously differentiable function.
https://www.desmos.com/calculator/91xdbwxaxv
Bezier curve
De Castelau algorithm, Bernstein form, polynomial form, matrix form, derivatives and curvature of Bezier curves.
https://www.desmos.com/calculator/5mxwdei16h
Hermite curve
Polynomial and matrix form, derivatives, curvature, osculating circle, quarter circle approximation.
https://www.desmos.com/calculator/ln1exvl9il
Cardinal curve
Polynomial and matrix form, derivatives, curvature, osculating circle, quarter circle approximation.
https://www.desmos.com/calculator/06mclwqqur
Catmull-Rom curve
Polynomial and matrix form, derivatives, curvature, osculating circle, quarter circle approximation. (Cardinal curve with tension 0.5)
https://www.desmos.com/calculator/z9slwnkvle
Rational Bezier curve
Circle, ellipse, parabola and hyperbola as rational Bezier curves in homogeneous coordinate matrix form.
https://www.desmos.com/calculator/j3bnviwjqv
R3
Sinoidal wave
Sinoidal wave in temporal, spatial and spatiotemporal representation
https://www.desmos.com/calculator/lowmmrrnk2
https://www.geogebra.org/classic/mwypcp4a
R4
Circular wave
Sinoidal oscillating membrane in canonical cross section views
https://www.desmos.com/calculator/piocwdyyo4
Flat wave
Sinoidal flat wave in canonical cross section views
https://www.desmos.com/calculator/f1faftq0mt
Polarized wave
Elliptical, circular and linear polarization of a sinoidal wave in cross section view
https://www.desmos.com/calculator/tcirqdnyt5
C1
Complex number arithmetic
https://www.desmos.com/calculator/7iak1wn5zg
Complex trigonometric functions
Trigonometric functions of complex values in the complex number plane: Sine, cosine, tangent, cotangent, secant, cosecant. Application to parametric line (grid), circle, and square.
https://www.desmos.com/calculator/nztgf6wjzu
