You are here:

Advanced Math/Model Railroads with Different Geometrical Shapes.

Advertisement


Question
QUESTION: Dear Prof Randy

http://en.wikipedia.org/wiki/List_of_geometric_shapes
http://en.wikipedia.org/wiki/Toy


Straight line segments
----------------------

http://en.wikipedia.org/wiki/Cyclic_polygon
http://en.wikipedia.org/wiki/Balbis
http://en.wikipedia.org/wiki/Pentagon
http://en.wikipedia.org/wiki/Octagon


Curved
------

http://en.wikipedia.org/wiki/Ellipse
http://en.wikipedia.org/wiki/Reuleaux_triangle
http://en.wikipedia.org/wiki/Sphere
http://en.wikipedia.org/wiki/Pentagram

Not composed of circular arcs
-----------------------------

http://en.wikipedia.org/wiki/Archimedean_spiral
http://en.wikipedia.org/wiki/Astroid
http://en.wikipedia.org/wiki/Super_ellipse
http://en.wikipedia.org/wiki/Tomahawk_(geometric_shape)


Do you feel by using different types of Geometrical Shapes viz Ellipse, Pentagon, Astroid etc can help in modeling different types of Railroads i.e. aid in actual construction of new rail routes as well as help in constructing railroads toys for the same.  

Awaiting your reply,

Thanks & Regards,
Prashant S Akerkar

ANSWER: I think using interesting, non-standard curves for toy railroad tracks is a great idea. Especially if the curves intersect and multiple trains are in motion. Perhaps an easily configured, flexible track could be used to experiment with the different shapes.

---------- FOLLOW-UP ----------

QUESTION: Dear Prof Randy

Thank you.

http://en.wiktionary.org/wiki/railroad
http://en.wikipedia.org/wiki/Rail_transport
http://en.wikipedia.org/wiki/List_of_geometric_shapes
http://en.wikipedia.org/wiki/Toy
http://en.wikipedia.org/wiki/PC_game
http://en.wikipedia.org/wiki/Video_game

Also is it possible to design and develop new computer games and video games modeling new rail routes/tracks ?.

Awaiting your reply,

Thanks & Regards,
Prashant S Akerkar

Answer
The first thing that comes to mind is to have the players be given a choice of possible routes that have several segments that are different lengths, speeds (eg., going up or down hill or around curves) and sources of delay. The players could drive the train along whatever segments they want that connect start to end. The players would run (adjust) the train at whatever speed they want along the way. The speed would affect energy consumption (cost), possible accidents and delays, etc. that would have a random component (likelihood of occurring as a function of speed). Each segmented route would have stops where the train has to load/unload pasengers, the time for which would also depend on how late or early the train is. Lengths of trains could be selected (and added/subtracted to) which would affect speed and energy consumption but also increase revenue (more freight/passengers) Routes could also intersect so that one train might have to wait for its opponent if the opponent is crafty and gets to the junction at just the right time. The winner is whoever get to the finish first with the most profit (freight delivered - energy consumed times on-time metric). Etc.

Advanced Math

All Answers


Answers by Expert:


Ask Experts

Volunteer


randy patton

Expertise

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

Experience

26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

Publications
J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

Education/Credentials
M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

Past/Present Clients
Also an Expert in Oceanography

©2016 About.com. All rights reserved.