Some math problems and calculations that Daniel found had a certain beauty


Derivation of the Law of Sines and the Law of Cosines for spherical Trigonometry

Derivation of the Law of Sines and the Law of Cosines for spherical Trigonometry is an intresting paper that came from playing with 3-dimensional rotation matrices. It gives a unique and original technique for deriving these two well known laws.


Estimation of Structured Coviance Matrices

A joint paper published in connection with consulting work Daniel did for John Burg. Estimation of Structured Coviance Matrices


Quantization in Clifford Space-Time

Quantization in Clifford Space-Time
and
Problems in Group Theory


PhD dissertation, Dept. of Physics, University of California, Los Angeles, 1966

Professor Robert Finkelstein, Chairman
Professor Robert J. Blattner
Professor Stevan A. Moszkowski
Professor David Saxon
Professor V. S. Varadarajan

University of Michigan Microfilm .


Canonical Root Vectors of SUn

Canonical Root Vectors of SUn

Journal of Mathematical Physics, Vol. 8, No. 1, Jan. 1967

Abstract
The present paper extends the study of SUn to the determination of particular root vectors and fundamental weights. The root vectors are chosen so as to show explicitly the canonical nesting of subgroups SUn >SUn-1 x U1 >SUn-2 x U1, etc. Explicit matrix representations of the fundamental representations are given. The results are all dependent upon the use of n vectors which define the fundamental region of SUn. Eigenvalues of fundamental invariant operators are also given in terms of these n vectors.


Representation Functions of the Group of Motions of Clifford Space

Representation Functions of the Group of Motions of Clifford Space

Journal of Mathematical Physics, Vol. 8, No. 1, Jan. 1967

Abstract
We find the representation functions of the group of motions of the three-dimensional Clifford space and of the three-dimensional Einstein space. These functions are generalizations of spherical and cylindrical waves of three-dimensional Euclidian space and reduce to these familiar functions in the Euclidian limit. The generalizaion of the plane wave is also found.


Random Walks in Space and Time

A problem that Daniel worked on periodically over a number of years and continues to work on. An early paper is now being revised.


Closed Expressions for Finite Transformations

This is an unpublished paper that emerged during Daniel's PhD studies. Closed Expressions for Finite Transformations


The Anelemma

These calculations were done during the development of the Wenger Sundial.

The analemma shows a relationship between the sun's declination and the difference between sun time and mean time. This relationship is of importance in designing a sundial that is to read mean sun time or clock time.

C language computer program to calculate the analemma using two different methods. Analemma Calculation

Analemma data generated by the above calculation. Analemma Data

Analemma data projected onto a sphere as seen from the outside of the sphere.

Analemma data projected with arrows showing seasonal motion of the sun.

A really nice photo of the Wenger Sundial

The Wenger Sundial

Stacks Image 78

Photo of the Analemma (as seen from the surface of the earth and as seen over a year long time period.)
Courtesy of the photographer, Dennis di Cicco and
Sky & Telescope magazine.