This site is ideas I have worked on or are working on.
You can view the categories by clicking on an item above. The title
“HyperdimensionalSpace” comes from some of my studies in cosmology. I
have recently finished 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 expanding 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.
-3D Folded Hexagram: This is a geometric object that I
discovered in the year 2000. It has interesting symmetry and
self-similar scaling properties. A discussion of the 3D folded
hexagram and its construction is presented along with various images
of the a 3D folded hexagram 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 circumference of the other.
HyperDimensionalSpace.com
Paul K. Sherard
3D
Folded Hexagram