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Geometry/Octagonal Chess Board

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Question
QUESTION: Dear Prof Azeem

The Chess board is a square having 64 Squares.

Is it possible to design and Construct a Octagon chess board where the board is divided into 64 Squares?.

Thanks
Prashant

ANSWER: Hi Prashant,

64 squares fit perfectly into a large square in an 8 by 8 arrangement.  However, squares do not fit perfectly into an octagon, by virtue of the oblique edges.  It may be possible to have such a board if we agree to waste some space along the oblique edges.  However, there would likely need to be some rule changes to properly accommodate a board of that shape.

Regards,
Azeem

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

QUESTION: Dear Prof Azeem

Thanks.

Which Other Polygons or other Shapes can be evaluated for having the Chess board divided into 64 Squares?.

Thanks
Prashant

Answer
Hi Prashant,

For the reasons mentioned above, it is difficult to have any shape that has edges that are oblique.  A rectangle or a plus sign might be interesting.  Having "holes" in the board could also be something to experiment with.

Regards,
Azeem

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Azeem Hussain

Expertise

I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.

Experience

4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

Publications
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry

Education/Credentials
Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.

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