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a theory about moth navigation is that moths fly at a constant angle relative to a light source.

a particular moth flies at 50 degrees to the light source,L, and it measures its bearing 10 times in one revolution.
Hint:one revolution is 360 degrees. 10 times makes the angle R1 L R0 equal to 360/10 (R1 here means the distance between L and the starting point of the moth. R2 is the distance between L and the first time the moth measures its bearing.)

1.)what happens if the number of times the moth measures its bearing increases to a very big number??

2)what does the limiting value appear to be?

3) what will the flight path be for x-->infinitive?

i drew a diagram for question 1 and figured out that as the number of times the moth measures its bearing increases to a very big number, the circle will get smaller and the moth will fly to the light sooner.but i can't figure out a formula for this...

i do not get question number 2.
question 3 is very similar to question number 2 right?? but i am still a little bit confused.=(

i have also worked out a formula for R1 in terms of R0:
R1=R0 times sin50/sin94)

so R(n) for all path is:
(let the angle the moth flies to the light source be A, and let times measured in one rev be B)

R(n)=sinA/sin{(360/B) +A}

i could try out question 1 and 3 by changing the value of B in that formula, but i don't know how to make a formula for question 1 and 3 by doing so...

I am really sorry if this looked very messy...but i will be so happy if some one can help me!thanks!! =)

  • Maths -

    ya u do this by eating some moths, there ya go

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