This site is ideas I have worked on or are working on. You can view the catagories by clicking on an item above. The title “HyperdimensionalSpace” comes from some of my studies in cosmology. I have recently fiinished a paper modeling the expansion of the universe. Click on icons above for more details.

- Modeling the expansion of the universe: This describes a visual model of the exapnding universe I have been working on for a number of years. The model yields insight into many o]f the characteristics of expansion including, light cones, the cosmological horizon, Hubble sphere, redshift, time dilation, and the evolution of proper distance. A version of this research was presented as a poster at the 2015 IAU XXIX General Assembly in Honolulu Hawaii. A pdf version of the latest version of the paper is also available.
-The Pyrard:
This is a new geometric object that I invented. It has interesting symmetry and self-similar scaling properties. A discussion of the pyrard and its construction is presented along with various images of the pyrard itself.
-Quasi-stable orbits: These “orbits” are related to fractal geometry, namely the Mandelbrot set. Included is a discussion of how these orbits are generated, some selected images, and my publication on the topic which can be downloaded.
-Elevation Angles: A thorough discussion on how objects (such as mountain peaks) can be seen over an observer’s horizon. A simple formula is presented along with a detailed derivation and discussion that can be downloaded.
-Equal Areas Problem: Shows the mathematical solution to the problem of finding the equal-area intersection of two circles, one centered on the cicumference of the other.
Paul K. Sherard
Equal Areas Problem
Modeling the Expansion of the Universe