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QUESTION: Hi I wonder if you could help me with a problem associated with my pastime of geocaching. If you started from a centre point and created a golden spiral based on the Fibbonacci numbers,at what point would it intersect a circle whose radius was 444 metres from the same starting point,ie: degrees .Scale 1 =1 metre Thanks for any help
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Hello John,
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The equation for the Golden Spiral is (in polar form): r=a*e^(b*theta),
where b=ln(phi)/(pi/2) with phi=golden ratio=(1+sqrt(5))/2 and "a" is
a constant. So, it depends on the value of "a" (the scaling factor).
Taking a=1, gives the equation: r=e^(b*theta)...setting that equal
to 444 gives: e^(b*theta)=444 ==> theta=ln(444)/b or about 19.8983 radians.
19.8983 radians is about 1140.1 degrees...or at about the 60.1 degree angle
(after subtracting 3*360). See attached image for the graphic.
I hope this helps.
Abe
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Answers by Expert:
Abe Mantell
Expertise
Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!
Experience
Over 15 years teaching at the college level.
Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.
Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook
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