temarimath.info
devoted to the study of temari and mathematics
TemariMath site glossary
This is a listing of terms used in the Temari Math website. Italicized words within definitions are listed elsewhere on the page. It is not intended to be exhaustive, but if you note something in the site that you feel needs an entry here, please send me an email: temari@zymurlogic.net.
In several of the entries I have included links to the MathWorld site. I have found that they have very good diagrams to illustrate certain words, although in most cases the math there is more involved than is needed for understanding this site.
- all-over design
- a temari design where the stitching and design threads completely cover the surface of the ball. There are no unstitched areas.
- C4
- a temari division having at most four angles at a vertex and six equally spaced 4-way verticies. A C4 division is identical to the Simple 4 with obi. Since all temari divisions have multiple 4-way intersections, a C4 is better named as an S4 with obi and is usually referred to in that way. Mathematically it is better placed in the S4 with obi category but is sometimes referred to as a C4 in order to complete the set of combination divisions.
- C6
- a temari division having at most six angles at a vertex and eight equally spaced 6-way vertices.
- C8
- a temari division having at most eight angles at a vertex and six equally spaced 8-way vertices.
- C10
- a temari division having at most ten angles at a vertex and twelve equally spaced 10-way vertices.
- combination division
- a temari division that has multiple verticies of the same type placed around the sphere at equal distances. For example, a C10 has twelve 10-way vertices placed so that each is the same distance from the others around it. There are four combination divisions: the C4, C6, C8, and C10. Mathematically speaking the C4 is better placed in the simple with obi division category but is included here for completeness.
- compound polyhedron
- a polyhedron made up of two or more other polyhedra arranged to penetrate each other so that the vertices of one emerge from the surface of the others.
- congruent
- having equal size and equal shape.
- duality
- a relationship between polyhedra where the center of the faces of one polyhedron are the vertices of its dual. The cube and octahedron are duals of each other. The tetrahedron is a unique case because its dual is another tetrahedron.
- edge
- a line segment that makes up the side of a face on a polyhedron or the side of a polygon. There's a nice diagram at MathWorld.
- face
- a 2-dimensional shape (polygon) that makes up the sides of a polyhedron. There's a nice diagram at MathWorld.
- great circle
-
a circle drawn on the surface of a sphere at its widest point. Another more precise way of defining it is to consider passing a plane through the center of a sphere. The resulting line on the surface of the sphere is a great circle. Here are some properties about spheres and great circles that might be useful:
- Two great circles will intersect on a sphere in exactly two opposite points.
- Given any two (not opposite) points on the sphere there is exactly one great circle going through both of them.
- The shortest distance between two points on a sphere is along the short segment of the great circle connecting them.
- lune
- a shape on the surface of a sphere having two vertices and edges. It looks like a section of an orange. It is the shape created when stitching a spindle in temari. There's a picture at MathWorld.
- multi-pole marking
- a C10 that has been further divided to create many poles (or intersections with more than 4 angles), with small pentagons and hexagons formed as the result.
- negative space
- parts of a temari that are left unstitched allowing the mari wrap to show. A design where the focal point is the unstitched shapes is called a negative space design. Here is an example:
- Platonic Solids
- a set of convex polyhedra with congruent regular polygons for faces: the cube, tetrahedron, octahedron, icosahedron and dodecahedron. See http://mathworld.wolfram.com/PlatonicSolid.html.
- polygon
- a two dimensional closed shape with sides made up of line segments
- polyhedron (plural: polyhedra)
- a three-dimensional solid made up of a collection of polygons joined at their edges. A convex polyhedra has no indentations.
- radians
- a unit of measure for angles based upon a circle's radius. 90 degrees = π/2, 180 degrees = π and 360 degrees = 2π
- regular polygon
- a two dimensional shape with equal sides and equal angles evenly distributed about it's center. It is what is often thought of as a perfect shape. Here are a regular triangle, square, pentagon and hexagon:
- S4 with obi
- a specific simple with obi temari division with four sections and an equator line. Sometimes called a C4.
- similar shapes
- shapes that have corresponding angles equal to each other
- simple with obi
- a temari division where all the lines intersect at the N and S poles with an added equator (obi) line. The naming convention is a capital S followed by the number of angles (or sections) at the N or S pole and the words 'with obi'. The picture on the left is an S12 with obi. The picture on the right is an S16 with obi (some of the marking lines are invisible).
- simple without obi
- a temari division where all the line intersect at the N and S poles only; there is no equator line. The naming convention is a capital S followed by the number of angles (or sections) at the N or S pole. The picture on the left is an S10 and has pins where the equator (obi) would be. The picture on the right is an S6. Sometimes you will see it labeled as 'S6 no obi' to make clear that there is no equator line.
- spindle
- a temari stitching technique that utilizes two stitching points to create a lune shape
- stretch the points
- a stitching technique where the distance between stitches gets greater as the points of a shape gets sharper. It is usualy accomplished by laying the thread along the line and looking at where it crosses the marking line to take the stitch.
- supplementary
- an angle is said to be supplementary to another angle (or group of angles) if they add to 180°. Graphically this means that together they will make a straight line. There's a nice diagram at MathWorld.
- support lines
- lines placed on the temari in addition to the original division to create shapes or points necessary for a given temari design. These may or may not be great circles.
- temari division
- a finite collection of great circles applied to the sphere such that they divide the surface into congruent shapes. (See also support lines and temari marking.)
- temari marking
- lines on a temari used as the basis for the design stitching. A marking may be the same as a division or it may include support lines. Sometimes markings are done invisibly so that they do not show on the finished temari. Note: in a special case a marking may consist of a S0 or S-naught division with support lines.
- tile the sphere
- place shapes on the sphere so as to cover the whole surface without overlapping.
- tiling
- a particular arrangement of specific shapes that repeat across a surface to cover it completely without overlaps.
- vertex (plural: vertices)
- 1. A point where two or more lines intersect, often referred to as an n-way vertex where n is the number of angles at the vertex.
- 2. The corner point of a shape for example, a pentagon has five vertices.
- 3. A corner on a polyhedron. There's a nice diagram at MathWorld.
Thank you to the wonderful people at mathworld.com for providing such a complete and thorough math resource. I have linked to it for those definitions that seemed to need a little more than I could provide.