## Videos | IsiXhosa

### The Möbius Band

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

### Exponential Ducks

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

### Thales' Theorem Part 1

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.

### Twin halves

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

### Traffic Lights

Different ways of stacking coloured blocks are investigated.

### Equal Areas

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

### Matchstick Squares

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.

### Difference of two squares

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

### Sum of odd numbers

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

### Area of a trapezium

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

### Area of a rhombus

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

### Rectangular products

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

### The Theorem of Pythagoras #2

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.

### Interior angles of a triangle

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.

### Tile patterns

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

### The Theorem of Pythagoras

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.

### Palindromic sums

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

### Viviani's Theorem

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.

### Hubcap geometry

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

### Interior angles of a triangle #2

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

### Sum of two squares

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

### VITALmaths

The VITALmaths and VITALmathsLIC site consists of a databank of short and funky video clips that specifically interrogate the conceptual aspects of a mathematical idea, process or concept. Some of the video clips contain strategic dialogues to encourage appropriate mathematical talk and conversation.

You are here

### SANDBOXmaths

SANDBOXmaths is a collection of more experimental video clips done by students in their mathematics teacher-training classes and researchers wishing to use specific video clips in their teaching and research.

### APPLETmaths

The APPLETmaths site consists of a selection of GeoGebra applets that were developed by students and researchers for their research projects.