# Visual Technology for the Autonomous Learning of Mathematics

Best viewed with VLC media player

### isiXhosa

The Möbius Band The Möbius Band, a curious one-sided surface, is explored. The Möbius Band - English - mp4 The Möbius Band - Deutsch - mp4
Exponential Ducks An exponential sequence (1 ; 2 ; 4 ; 8 ; ...) is generated and investigated through the process of doubling.
Thale's 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.     Thales' Theorem Part 1 - Deutsch - mp4
Twin halves Different ways of splitting a square array of blocks into two identical sections are explored. Twin halves - English - mp4 Twin Halves - Deutsch - mp4
Traffic Lights Different ways of stacking coloured blocks are investigated. Traffic Lights - English - mp4 Traffic Lights - Deutsch - mp4
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.

PCs

Mobiles

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

PCs

Mobiles

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

PCs

Mobiles

A third minus a fifth A visual approach is used for the subtraction of a smaller fraction from a larger one. The example used is a third minus a fifth.

PCs

Mobiles

PCs

Mobiles

A third plus a quarter A visual approach is used to support the conceptual understanding of the addition of two fractions. The example used is a third plus a quarter.

PCs

Mobiles

PCs

Mobiles

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

PCs

Mobiles

PCs

Mobiles

Angles of a polygon The movement of a paperclip on the sides of a triangle points the way to the generation of a formula for the sum of the interior angles of a polygon.

PCs

Mobiles

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

PCs

Mobiles

PCs

Mobiles

Visible faces The general formula 4x+1 is modelled in terms of the number of faces visible when cubes are stacked on top of one another.

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.

PCs

Mobiles

PCs

Mobiles

What's in the box? #2 This video clip models the solving of simultaneous equations through a process of logical reasoning without the introduction of algebra.

PCs

Mobiles

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.

PCs

Mobiles

PCs

Mobiles

What's in the box? #3 Building on from previous "What's in the box?" clips, variables are now introduced to represent unknown quantities.

PCs

Mobiles

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

PCs

Mobiles

PCs

Mobiles

The Theorem of Pythagoras #3 Another striking visual approach is used to demonstrate the Theorem of Pythagoras.

PCs

Mobiles

A quarter plus a third A model of a rectangle is used to visualise the sum of two fractions, a quarter and a third.

PCs

Mobiles

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.

PCs

Mobiles

PCs

Mobiles

Discovering right-angled triangles Squares are used to form the edges of triangles in order to discover Pythagorean triples.

PCs

Mobiles

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

PCs

Mobiles

PCs

Mobiles

Sums of cubes This video clip illustrates the result that the sum of the first n cubes is the square of the nth triangular number.

PCs

Mobiles

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.

PCs

Mobiles

What's in the box? Matches and different coloured matchboxes are used to model the concept of variable.

PCs

Mobiles

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

PCs

Mobiles

Hidden faces This video clip explores the number of faces which are hidden from view when cubes are stacked on top of each other.   Hidden Faces - Deutsch - mp4
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.

PCs

Mobiles

PCs

Mobiles

PCs

Mobiles

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?

PCs

Mobiles

PCs

Mobiles

Ninety-nine

The film suggests the following conjecture: If you take a two-digit number and subtract its reverse, and then take the answer and add its reverse, then the result is always 99     e.g. 42-24=18, 18+81=99

Winning with chance #1 The film demonstrates a simple game based on the statistics of chance. The video clip makes use of specific activity sheets.
Winning with chance #2  The film suggests an extension to the video clip “Winning with chance #1”.
Pythagorean triples   This video clip explores Pythagorean triples.
Train Maths #1 This video clip explores the drawing of scale diagrams through the use of model railway tracks. The clip is only available in German, and refers to specific activity sheets.
Train Maths #2 This video clip makes use of model railway tracks to explore basic algebra. The clip is only available in German, and refers to specific activity sheets.
Train Maths #3 This video clip is an extension of “Train Maths #2” and again explores simple algebra. The clip is only available in German, and refers to specific activity sheets.
Train Maths #4 This video clip is an extension of “Train Maths #3” and explores simple algebraic operations. The clip is only available in German, and refers to specific activity sheets.

Last Edited:  9 November 2012  By:    Print

©2012 Rhodes University • Rhodes University, P.O. Box 94 Grahamstown 6140 South Africa
Tel: +27-46-603-8111 • Fax: +27-46-603-7350 • Email: registrar@ru.ac.zaTerms & ConditionsPROATIA