Main menu

**Getting on to a definition (Cubing De Tinseau/De Malves):**The diagrams above

Using these values the areas of the faces are found to be as follows (units not shown):

Squaring of which gives: 27 64 125 216

Of which the cube roots give 3 4 5 6

Of which the cubes give 27 64 125 = 216 or 3^3 + 4^ 3 + 5^3 = 6^3

Accordingly, going upwards through the above, Alternative Definition of A Theorem on Cubes underlying Swannies Theorem: Regarding a tetrahedron with a trirectangular vertex the sum of the cubes of the cube roots of the squares of the areas of the faces intersecting at the vertex equals the cube of the cube root of the square of the area of its base. (Rather see the easier definition below in bold lettering)

The following table use these values:

Area of face: 5,2 cm2 8,0 cm2 11,2 cm2 14,7 cm2

Base of prism: 5,2 cm2 8,0 cm2 11,2 cm2 14,7 cm2

Height of Prism: 5,2 cm 8,0 cm 11,2 cm 14,7 cm

Volume of Prism: 27 cm 3 64 cm 3 125 cm 3 = 216 cm 3

To provide for De Tinseau's projections it obviously needs some extra wording.

Home Page | Personal | Equations | Pyth.& box | Definitions | Models | Art | II and III | IV and V | VI to X | Bra & Ball | Potpourri | Squaring | ------------ | Story | Story | Story | Golden R | Tribonacci | Fairy 1 | Fairy 2 | Fairy 3 | General Site Map