Learn maths: circles, diameter, radius, circumference, cylinders, pi, area, surface area, volume. Conic sections (circle, ellipse, parabola, and hyperbola, created by the intersection of a plane with cone). Formulae and equations. Cartesian coordinates (XYZ axes). Sine wave, cosine wave, and tangent graphs. Pythagoras' Theorem. Steampunk style maths engine. Solids of revolution.
Cartesian Coordinates. XYZ axes. This animation shows how Cartesian coordinates can describe a point along a line, in a plane, or in a space. The video begins with a square sheet of paper that develops a grid pattern of fine blue lines. A central red point (origin) appears. Then X and Y axes emerge (positive are brass coloured, negative are dark red). The positions +10 and -10 are indicated along the number lines. A point (purple) moves to position 7 along the X axis, and then to position 5 on the Y axis. These coordinates are written as (7,5). Then a blue point moves to position -5 on the X axis, and then to -9 on the Y axis, so its coordinates are (-5,-9). Up until now, everything has happened in the plane of the sheet of paper. In fact, you can do all of this with a real piece of paper on a desk. Then the purple point moves upwards, above of the piece of paper, and the vertical (Z) axis emerges. The point stops at 8 units above the paper (position 8 on the Z axis), giving the purple point coordinates of (7,5,8). Shadows of the purple point are cast on each of the three perpendicular planes. This explains how the three coordinates (x,y,z) can specify a point anywhere in three dimensional space. All sorts of useful mathematical operations can be done using these coordinates.
Cartesian Coordinates. XYZ axes. This animation shows how Cartesian coordinates can describe a point along a line, in a plane, or in a space. The video begins with a square sheet of paper that develops a grid pattern of fine blue lines. A central red point (origin) appears. Then X and Y axes emerge (positive are brass coloured, negative are dark red). The positions +10 and -10 are indicated along the number lines. A point (purple) moves to position 7 along the X axis, and then to position 5 on the Y axis. These coordinates are written as (7,5). Then a blue point moves to position -5 on the X axis, and then to -9 on the Y axis, so its coordinates are (-5,-9). Up until now, everything has happened in the plane of the sheet of paper. In fact, you can do all of this with a real piece of paper on a desk. Then the purple point moves upwards, above of the piece of paper, and the vertical (Z) axis emerges. The point stops at 8 units above the paper (position 8 on the Z axis), giving the purple point coordinates of (7,5,8). Shadows of the purple point are cast on each of the three perpendicular planes. This explains how the three coordinates (x,y,z) can specify a point anywhere in three dimensional space. All sorts of useful mathematical operations can be done using these coordinates.