MSD

Storage bytes are placed symmetrically on a disk of radius 7cm. No two storage locations can be closer (arc length on the circle on which they are placed, not straight line) than 0.1cm. Bytes are distributed in concentric circles on rays emanating from the center of the disk. Approximate the location of the innermost circle of bytes that would maximize the total number of bytes on the disk. No data are stored on the outer edge of the disk.

dimbulb

i'm guessing no one is answering because no one understands the problem.

I'm not sure how this data is stored. Perhaps you can provide us with a picture?

bytes are in concentric circles... yet they are on a ray?????

saltfish

Can you give us an idea of the area that each byte would occupy?


-SF

MSD

-bytes are stored on the intersection or a ray and a circle
-each byte is a point with an area of 0
-the distance between circles, despite irregularities in the drawing, is 0.1cm
-the length of the arc between two data bytes on the circle is 0.1cm, therefore two bytes can be less than 0.1cm from each other, as long as the arc length is 0.1cm

lordjeebus

I believe that the innermost circle of bytes has radius 3.5 cm.

Proof pending.

lordjeebus

Proof:

r = radius (in mm) of the smallest ring.

The number of bytes per ring = (Innermost ring circumference)/(spacing) = (2*pi*r)/(1 mm) = 2*pi*r

The number of rings = 70 mm - r

The number of bytes b(r) = 2*pi*r*(70-r)

At maximum number of bytes, the derivative of b(r) = -4*pi*r + 140*pi = 0; r = 35 mm

This is a maximum, not a minimum b/c the second derivative is negative.

MSD

herostar

Sorry I can't help w/ the math...

mrselfdestruct... I see you're a turbo lover... me too. what kind of car do you have?

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Grothendieck

Congratulations, lordjeebus.
I like your last sentence

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