Points and solids in 3D coordinates
Place points in 3D coordinates, rotate the view and calculate distances with Pythagoras' theorem.
MathematicsGrade 10–13 · University
Analytic geometry
Points, vectors, lines, planes and spheres in space – rotatable in 3D, with relative positions and distances.
Link to the German educational standards (KMK)
- L4Space and shape
- K4Using mathematical representations
- K5Working with mathematical objects
Vectors in space
Grade 10–12
Adding and scaling vectors (3D)
Drag vector arrows in space, add them and multiply them by numbers. The calculation is shown alongside in column form.
Dot product and cross product
The dot product tells you the angle between two vectors; the cross product gives a perpendicular vector and an area.
Lines, planes and spheres
Grade 11–13
Lines and planes in space
A point travels along a line through space, two vectors span a plane. Parametric, normal and coordinate forms all describe the same thing.
Relative positions and distances in space
Do the lines meet, run parallel or pass each other by? In a 3D space you can turn, intersections, angles and distances become visible.
Spheres, lines and planes
A plane cuts the sphere in a circle, touches it at a point or misses it entirely. Including the equation of the sphere and the tangent plane.
Matrices (university)
Grade 12–13 · University
Matrices as linear maps
Two arrows decide everything: wherever they point, the matrix rotates, stretches or reflects the whole grid.