Truncated geometry on the circle

Special Geometry and Compactification on a Circle

We discuss some consequences of our previous work on rigid special geometry in hypermultiplets in 4-dimensional Minkowski spacetime for supersymmetric gauge dynamics when one of the spatial dimensions is compactified on a circle.

UCLA Math Circle: Projective Geometry

On the real number line, a point is represented by a real number x if x is finite. Infinity in this setting could be represented by the symbol ∞. However, it is more difficult to calculate with infinity. One way to resolve this issue is through a different coordinate system call homogeneous coordinate. For the real line, this looks a lot like fractions. Instead of using one number x ∈ R, we wil...

Apollonian Circle Packings : Geometry and Group Theory

Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We observe that there exist Apollonian packings which have strong integrality properties, in which all circles in the packing have integer curvatures and rational centers such that (curvature)×(center) is an integer vector. This series of papers explain such...

Affine circle geometry over quaternion skew fields

We investigate the affine circle geometry arising from a quaternion skew field and one of its maximal commutative subfields.

Global Optimization in Geometry | Circle Packing into the Squarep