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Number Theory/Tunnel Shapes.

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Question
Dear Prof Vijilant

Can we Design tunnels without a circular shape?.

Examples - Triangle, Square, Rectangle, Kite, Rhombus etc?.

Thanks
Prashant

Answer
Hello Prashant
Are you sure all tunnels have a circular shape?  They have probably been circular in section initially, because they were drilled. They are holes.  How do you make a hole in a piece of wood?  With a drill.
And that is how most tunnels are begun.  And then, of course, the bottom is filled in after burying cables etc.  But of course, a different drill could be used.  By using the idea of curves of constant width, a square hole could be drilled. Then a rectangular tunnel by two adjacent square tunnels. This was done by Watts Brothers Tool Works in Wilmerding, PA.  They make other drills, that drill sharp-cornered holes in the shape of pentagons, hexagons, and even octagons. Of course, it might be difficult to scale up to the size needed for a tunnel, but the possibility is there. And perhaps the strongest roof of a tunnel should be an inverted catenary.  I can't see any use for such shapes as a kite.
Best wishes
vijilant

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Vijilant

Expertise

Most questions on number theory, divisibility, primes, Euclidean algorithm, Fermat`s theorem, Wilson`s theorem, factorisation, euclidean algorithm, diophantine equations, Chinese remainder theorem, group theory, congruences, continued fractions.

Experience

Teacher of math for 53 years

Organizations
AQA Doncaster Bridge Club Danum Strings Orchestra Doncaster Conservative Club Danum Strings Orchestra Simply Voices Choir Doncaster TNS mystery shopping St Paul's Music Group Cantley

Publications
Journal of mathematics and its applications M500 magazine

Education/Credentials
BSc (Hons) Liverpool (Science). BA (Hons) OU (Mathematics)

Awards and Honors
State Scholarship 1955 Highest Score in Yorkshire on OU course MST209 50 prize First class honours in OU BA Mathematics

Past/Present Clients
I taught John Birt, former Director of the BBC in 1961. His homework book was the most perfect I have ever marked. And also the most neat. I could tell he was destined for great things. One of my classmates was the poet Roger McGough, and I have a mention in his autobiography.

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