First block

Set #1

Sunrise at Miletos

Feature scheme: 3D cude, 6n - 3 features all with 6 possible value per feature, 6x6x6 = 216 pictures.

Color scheme: Rising sun, square background, and the line can have 6 different shades.

Thales Theorem

Thales of Miletos (624-546 BC) was the very first Greece mathematician. Thales’s most famous discovery, still named after him, says that from any point on the circumference of a circle, the diameter always subtends a right angle. Thales’s theorem can actually be generalized to any chord, not just the diameter. Such a chord divides the circle into two unequal arcs. Any point lying on the larger of these arcs subtends the chord at a constant angle.

External link to the theorem: Wikipedia

Set #2

Quadrilaterals

Feature scheme: 3D pyramid, 8n - 3 features all with 8 possible values per feature, the first feature can take 8 values, the other two can take as many features as the current number of feature 1.

Color scheme: Four different colors with multiple shades.

Calculating the area of a quadrilateral

The size of a quadrilateral is determined as half of the product of its diameters.

Set #3

Pythagorean Theorem (extended)

Feature scheme: 4D cube, 4n - 4 features (number of tiles, colors) all can have four different values.

Color scheme: Four different colors with multiple shades.

Calculating the area of a quadrilateral

As a result of the very well know pythorean theorem (a^2 + b^2 = c^2) one can conlcude one additional interrelation. Namely, the square built on one side of right trinagle has the same area as the rectangle formed by hypotenuse and the projection of that side on the hypotenuse. (Ref: The Story of Mathematics)