THE GEOMETRY OFSOUTHERN AFRICAN COUNTRIES

Alexis van den Hoogen

Caroline Kelly

OUR FOCUS: SOUTHERN AFRICA

Democratic Republic of Congo

Tanzania

Angola

Zambia

Malawi

Namibia

Botswana

Zimbabwe

Mozambique

South Africa

Lesotho

Swaziland

LEBOMBO BONE

- Baboon fibula

- At least 35,000 years old

- Oldest mathematical instrument in the world

- Named for its location, Lebombo mountains in Swaziland

ISHANGO BONE

- Dated at least 20,000 BC

- Oldest attestation of the practice of arithmetic in human history

- Suggested use for keeping track keeping track of the

lunar/menstrual cycle.

- Incorporates multiplying, dividing and prime numbers.

FRACTALS

- Predominant design theme in African culture

- Not only true for architecture, but for many other material design and cultural practices as well.

-Although it does appear in places such as the Chinese culture and Southern India, fractal designs in Africa are culturally specific.

SIPATSI

- Straw woven handbags

-Traditionally made by women

- Symmetry being the key to all designs

- Must satisfy certain specific standards to be considered beautiful/good quality.

- The required number of coloured

strands needed to create this motif is

8, therefore the period shown is 8.

- To create a pattern for the gipatsi,

a common multiple of 8 for the

coloured strands is needed.

- The first pattern shown reflected on

the horizontal axis. If the pattern is

also horizontally translated, to the

left or the right by half of period

length, the pattern will return to the

original.

BUHLOLO

OKU-TALEKA-The motif does not have axial symmetry. The neck design belongs to type cn. The c stands for cyclic, from one position to the next it must be rotated 1/n times of a complete turn, so an angle of 360/n.

-The pattern shown is a decorated pot shown from below.

-There is a 9-fold rotational symmetry of the decoration. (n = 9)

LITEMA – MURALS

-Mostly from Sotho houses in South Africa. Many of the litema designs resemble furrows made in the earth when planting.

-Symmetry is one of the most fundamental features of a litema design. There is frequently axial or bilateral symmetry.

IKGHUPTA – MURALS

-The Ndebele women, from northern South Africa, also create murals.

-The difference between the two sets of murals is the characteristics of the geometric designs and additional painted lines.

“THE MATHEMATICIAN’S PATTERNS, LIKE THE PAINTER’S OR THE POET’S, MUST BE BEAUTIFUL. THE IDEAS, LIKE THE

COLOURS OR THE WORDS, MUST FIT TOGETHER IN A HARMONIOUS WAY. BEAUTY IS THE FIRST TEST: THERE IS NO PERMANENT PLACE IN THE WORLD FOR UGLY MATHEMATICS”

(HARDY, 1940, P. 84, 85)

Thank you!

EXAM QUESTION

When making a gipatsi:

A) You have 24 coloured strands, are you able to create a beautiful gipatsi?

Explain why or why not. If the answer is yes, what are all the possible periods?

B) You have 22 coloured strands, are you able to create a beautiful gipatsi?

Explain why or why not. If the answer is yes, what are all the possible periods?