I have placed your Presentation
Slides into the directory "ProjectPresentations"
If you would like to share yours, please send them to me.
Final Assignments:
-- For next class, prepare an "Elevator Speech" (60-90
seconds).
-- By December 11, write a Project Report
(2-4 pages; use some figures from your slides).
Is there a practical application for the
regular 4D polytopes?
I have not been able to think of one ...
Check the web for possible responses, e.g.,: Applications of Higher Dimension Formulas
The regular 4D polytopes are a piece of
pure mathematics.
Often it takes several decades before a new insight in
mathematics is used in some other discipline.
Another example of questionable usefulness:
Earlier in 2017 there was news of “The
largest known prime number:
2^74,207,281 - 1“
This number is
22,338,610 digits long.
It is estimated that there are about
10^17,425,163 prime
numbers less then the next smaller known prime.
That means we know only a fraction of about
10^-14 of all the prime numbers in this neighborhood.
Is this knowledge useful? Is mathematics
useful?
But mathematics can be beautiful!
By strict
logical reasoning one can derive new mathematical insights
that are irrefutable and not subject to later change.
By analogy
from 1-, 2-, and 3-dimensional spaces, we can derive 4- and
higher-dimensional spaces.
And then we can show unambiguously that in
4D-space there are exactly six totally regular polytopes.
No science or religion has this kind of
internal consistency and permanence.
All fields have some
Threshold Concepts
Regular
Polytopes in Four and Higher Dimensions (remainder)
If you are brave enough, look at: "A
10-Dimensional Jewel" PPT
Prepare Your "90-seconds Elevator Speech".
Please take the Course Evaluation survey.
Work on your final Project Reports: Due Dec. 11,
2017.