A circular hole has a stack of narrow boards next to it, all the length of the radius of the circle. There is nothing to attach the boards together with. What is the smallest number of boards it takes to have one span across the center of the circle?

Question

A circular hole has a stack of narrow boards next to it, all the length of the radius of the circle.  There is nothing to attach the boards together with.  What is the smallest number of boards it takes to have one span across the center of the circle?

anonymous · Answer

yup

amistre64 · Answer

well, an equi makes a hexagon around the perimeter

amistre64 · Answer

then i spose there are subsequents hexs till you approach a distance across that is less than r

amistre64 · Answer

do we account for enough of the boards to ledge against each other or assume a magical world of impossibilities?

anonymous · Answer

what do you mean by ledge?

amistre64 · Answer

have you ever leaned against a table to find out that you had in fact just missed the table so that you end up somewhere closer to the vacinity of the floor instead?

anonymous · Answer

I suppose you could form a cantelever, I wonder if that is less than the sphincter you were describing with hexagons

amistre64 · Answer

how wide are the boards?

anonymous · Answer

the boards are able to stack, consider that if they intersect, they are supported.

amistre64 · Answer

wider boards take fewer to count

anonymous · Answer

Depends on the size of the hole, which isn't given

amistre64 · Answer

no, that length, width is a different mater

amistre64 · Answer

im assuming thickness is moot

anonymous · Answer

it's proportinate

amistre64 · Answer

rxr then?

anonymous · Answer

that's too wide! no fair!

anonymous · Answer

Doesn't the problem statement say "narrow"?

amistre64 · Answer

narrow yes, but that is not very quantitative ;)

anonymous · Answer

this is the math forum, not physics, shouldn't there be a theoretical answer instead of a practical one?

amistre64 · Answer

i spose ....  just dont let osha find out

anonymous · Answer

Or should I ask philosophers instead?

amistre64 · Answer

im getting an a in philosophy class, so i should qualify for the position

amistre64 · Answer

whats the measures of a 30 60 90?

anonymous · Answer

1, 2, sqrt(3)

amistre64 · Answer

if r/2 = sqrt(3); what does 1 equal?

anonymous · Answer

shrinking hexes leads to 17, which is too many, try again

anonymous · Answer

1

amistre64 · Answer

i get r/2sqrt(3)

amistre64 · Answer

|dw:1318905432817:dw|

amistre64 · Answer

this mouse is awful

anonymous · Answer

I have an answer, but keep working on it, I'd like to know what you get.

anonymous · Answer

I used Geometer's Sketchpad

amistre64 · Answer

if i start from the middle and span outwards, i get this:
|dw:1318946471472:dw|

amistre64 · Answer

which adds up to 15

amistre64 · Answer

|dw:1318947344847:dw|