Videos | IsiXhosa

The Möbius Band, a curious one-sided surface, is explored.

An exponential sequence (1 ; 2 ; 4 ; 8 ; ...) is generated and investigated through the process of doubling.

When a semicircle is drawn such that its diameter is the hypotenuse of a right-angled triangle, the semicircle passes through all three vertices of the triangle.

Different ways of splitting a square array of blocks into two identical sections are explored.

Different ways of stacking coloured blocks are investigated.

Six different shapes are investigated in terms of their areas. The video clip concludes by showing why all six shapes have the same area.

A matchstick pattern based on a linear sequence is investigated. Different deconstructions of the pattern lead to different but algebraically equivalent expressions for the general term.

A visual explanation is explored for the observation that 2²-1²=2+1; 3²-2²=3+2 etc.

A visual explanation is explored for the observation that 1 + 3 + 5 + 7 + … for n terms equals n².

The formula for the area of a trapezium is explored through a series of different visualisations.

Two alternative formulae for determining the area of a rhombus are investigated.

This video clip makes use of geometric algebra to give elegant visual support for the distributive law.

A proposal is made for a visual proof of the Theorem of Pythagoras.  The question is raised as to whether or not this constitutes a general proof.

This video clip investigates the sum of the interior angles of a triangle. A visually striking approach is used to show that these angles add up to 180 degrees.

This video clip explores the patterns and symmetry elements produced through tiling.

A proposal is made for a visual proof of the Theorem of Pythagoras.  The question is raised as to whether or not this constitutes a general proof.

Visual aspects of palindromic sums such as 1+2+3+4+3+2+1 are investigated.

Visually illustrates that for a point inside an equilateral triangle, the sum of the perpendiculars from that point to the sides of the triangle equals the altitude of the triangle.

Hubcaps are investigated in terms of their rotational and reflectional symmetry.

A visually appealing approach is used to show that the interior angles of a triangle add up to 180 degrees.

The following question is investigated: Is it possible to construct a third square whose area is the sum of two given squares?