THE GEOMETRIC STRUCTURE OF KUNTUNKANTAN
The central form in Kuntunkantan is the circle. A circle is a curved line which forms a continuous sequence, every point on which is an equal distance from a center. The centre itself being a point inside the circle from which all points on the circle are equidistant.
Kuntunkantan has five circles but if it is drawn in thick circular lines rather than a single, circular line, one can describe each circle as composed of an outer, black circle and an inner, white circle. Two circles, therefore, which are concentric, each having the same centre. In sharing the same centre, they are on the same plane, making them coplanar. In being concentric, the area or space between both circles is an annulus.
One can measure the distance from the centre to any point on the circle. That distance is the radius. The radius is half the diameter of the circle.
The diameter is the distance across the circle. It is twice the radius.
One can measure the distance around the circle to arrive at the circumference.
One can also measure the area of the region enclosed by the circle.
One can divide the circumference-the distance around the circle- by it's diameter-the distance across the circle. This operation always produces the same number. This number is called Pi and is approximately 3.142.
One can modify the circle by relating to straight lines so as to demonstrate other properties of the circle not evident in its unmodified form.
One could link any two points on the circle with a line segment to create a chord.
One could make a line pass the circle and touch it at just one point to create a tangent.
Or draw line that intersects the circle at two pints to create a secant.
Kuntunkantan has five circles but if it is drawn in thick circular lines rather than a single, circular line, one can describe each circle as composed of an outer, black circle and an inner, white circle. Two circles, therefore, which are concentric, each having the same centre. In sharing the same centre, they are on the same plane, making them coplanar. In being concentric, the area or space between both circles is an annulus.
One can measure the distance from the centre to any point on the circle. That distance is the radius. The radius is half the diameter of the circle.
The diameter is the distance across the circle. It is twice the radius.
One can measure the distance around the circle to arrive at the circumference.
One can also measure the area of the region enclosed by the circle.
One can divide the circumference-the distance around the circle- by it's diameter-the distance across the circle. This operation always produces the same number. This number is called Pi and is approximately 3.142.
One can modify the circle by relating to straight lines so as to demonstrate other properties of the circle not evident in its unmodified form.
One could link any two points on the circle with a line segment to create a chord.
One could make a line pass the circle and touch it at just one point to create a tangent.
Or draw line that intersects the circle at two pints to create a secant.
For more on Adinkra and mathematics see other Adinkra blogs in this series: www.adinkraheneone.blogspot.com and forthcoming postings in www.nyansapo.blogspot.com.
SOURCES
The general mathematical information applied to Kuntunkantan in this post is adapted from the wonderful site MathOpenReference at http://www.mathopenref.com/
and compared with the information in WolframMathworld at http://mathworld.wolfram.com/
and Wikipedia,the online encyclopedia,
as well as the essay by by Obeng-Aduasare, Yaw, "The Root Cause of Lack of Self-confidence In The Ghanaian Psyche" on GhanaWeb at http://www.ghanaweb.com/GhanaHomePage/features/artikel.php?ID=129590 where he describes the Adinkra symbol known as Adinkrahene in geometric terms.
Other useful sources that,like Obeng-Aduasare's essay, explore the mathematics of Adinkra are African Fractals by Ron Englash and "Symmetry and Dissymmetry in Mathematics Education: One View from England" by Mary Harris in Leonardo, Vol. 23, No. 2/3, New Foundations: Classroom Lessons in Art/Science/Technology for the 1990s (1990), pp. 215-223.
The work of Sylvester James Gates and Michael Faux in theoretical physics and others who use the mathematical technology they developed which they have named Adinkras and Adinkrammatics, is valuable,even though they claim only an indirect relationship between their work and Adrinkra.The relationship between their work and Adinkra consists in its use of thevisual exploration of mathematical properties through line permutations which bear an imaginative relationship to some Adinkra symbols,particularly those named Nyansapo and Epe.
Particularly helpful is Gates and Faux's first essay in this field "Adinkras:A Graphical Technology for Supersymmetric Representation Theory" at http://arxiv.org/abs/hep-th/048004 from http://arxiv.org/the open access site at Cornell University for papers in the quantitative sciences.
A search under Adinkras at the arXiv.org site and a Google search for Adinkra and Supersymmetry,the field they work on,yields a rich harvest which will further clarify their philosophy of relationships between visual form as represented by the line formations of what they call their Adinkra technology and mathematical exploration.
Gates's interviews,a number of them online, where he describes his work, and his DVD on his research "Superstring Theory: The DNA of Reality" with the Teaching Company: http://www.teach12.com/teach12.asp at http://www.teach12.com/ttcx/coursedesclong2.aspx?cid=1284 are also invaluable.
While the other sources mentioned here are directed to a greater or lesser degree at the layperson,and Gates DVD is meant for a general audience,the academic papers by Gates and his fellow scientists are exercises in the professional activity of cutting edge physics.
The general mathematical information applied to Kuntunkantan in this post is adapted from the wonderful site MathOpenReference at http://www.mathopenref.com/
and compared with the information in WolframMathworld at http://mathworld.wolfram.com/
and Wikipedia,the online encyclopedia,
as well as the essay by by Obeng-Aduasare, Yaw, "The Root Cause of Lack of Self-confidence In The Ghanaian Psyche" on GhanaWeb at http://www.ghanaweb.com/GhanaHomePage/features/artikel.php?ID=129590 where he describes the Adinkra symbol known as Adinkrahene in geometric terms.
Other useful sources that,like Obeng-Aduasare's essay, explore the mathematics of Adinkra are African Fractals by Ron Englash and "Symmetry and Dissymmetry in Mathematics Education: One View from England" by Mary Harris in Leonardo, Vol. 23, No. 2/3, New Foundations: Classroom Lessons in Art/Science/Technology for the 1990s (1990), pp. 215-223.
The work of Sylvester James Gates and Michael Faux in theoretical physics and others who use the mathematical technology they developed which they have named Adinkras and Adinkrammatics, is valuable,even though they claim only an indirect relationship between their work and Adrinkra.The relationship between their work and Adinkra consists in its use of thevisual exploration of mathematical properties through line permutations which bear an imaginative relationship to some Adinkra symbols,particularly those named Nyansapo and Epe.
Particularly helpful is Gates and Faux's first essay in this field "Adinkras:A Graphical Technology for Supersymmetric Representation Theory" at http://arxiv.org/abs/hep-th/048004 from http://arxiv.org/the open access site at Cornell University for papers in the quantitative sciences.
A search under Adinkras at the arXiv.org site and a Google search for Adinkra and Supersymmetry,the field they work on,yields a rich harvest which will further clarify their philosophy of relationships between visual form as represented by the line formations of what they call their Adinkra technology and mathematical exploration.
Gates's interviews,a number of them online, where he describes his work, and his DVD on his research "Superstring Theory: The DNA of Reality" with the Teaching Company: http://www.teach12.com/teach12.asp at http://www.teach12.com/ttcx/coursedesclong2.aspx?cid=1284 are also invaluable.
While the other sources mentioned here are directed to a greater or lesser degree at the layperson,and Gates DVD is meant for a general audience,the academic papers by Gates and his fellow scientists are exercises in the professional activity of cutting edge physics.
Comments