Geometry question
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Wmcmanus

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Question: How large does a hexagon need to be in order to fit a 15" circle inside of it? What I need to figure out is the exact length of each of the 6 sides.

Here is the situation: I'm trying to order a custom dust cover and Cloud 10 platform from Gingko Audio to fit my Shanling T300, which has a more or less (but not perfectly) round shape. The T300 measures anywhere from 13" to 13.5" across, so a 15" inner measurement of the hexagon-shaped dust cover will provide enough clearance on all sides. Unfortunately, they can't make a circle shaped cover.

Here's what the square cover looks like for the T200 to give you an idea of what I'm talking about.

I've tried to figure it out by sitting on the floor and forming various sized circles with an extra pair of speaker cables I have lying around, but I'm sure it's a simple math question for anyone who finished high school less than 25 years ago!
 
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nikongod

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from what i calcluated you need a hexagon with each side having an 8.66" inside length.

this allows the opposite (parallel) walls to be 15" appart on the inside. this will exactly fit a 15" circle.

woot. it makes me happy my engineeering degree goes to good use.
 
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drewd

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Trigonometry!

The right triangle has a height of 7.5", one angle of 30 degrees and one angle of 60 degrees.

The tangent of 30 degrees is about .577, so the length you're after is 2*.577*7.5= 8.66".

Pictures would explain it a lot better.

As an aside, when I started my EE degree, I sucked so badly at math that I had to start out with Algebra. Then trig. And neither of them counted for my degree


[EDIT: I guess I shouldn't start typing and then walk away...
]

-Drew
 
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Wmcmanus

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I'm not sure I understand exactly, but coming from two engineers, I'll defer to your judgment. I was thinking 7.5" sides would work but I guess that would be putting a somewhat smaller hexagon inside of a 15" circle, rather than putting a 15" circle within a somewhat larger hexagon!

What you're both saying is that a hexagon having 8.66" sides will fit a 15" circle within it? Correct?
 
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Wmcmanus

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Ok, rocket scientists! Here's another one for you:

If 8.66" is used for each side of the cover, how long should each side of the platform be to allow and extra 1/2" as a lip on the platform all the way around?

In other words, the platform is also going to be a hex shape. The CD player sits on the platform, and the cover then goes over the CD player, leaving an outer lip of 1/2" so that the cover can be taken on and off the platform rather easily without having to line everything up perfectly each time.
 
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The_Mac

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Quote:

Originally Posted by Wmcmanus
Ok, rocket scientists! Here's another one for you:

If 8.66" is used for each side of the cover, how long should each side of the platform be to allow and extra 1/2" as a lip on the platform all the way around?

In other words, the platform is also going to be a hex shape. The CD player sits on the platform, and the cover then goes over the CD player, leaving an outer lip of 1/2" so that the cover can be taken on and off the platform rather easily without having to line everything up perfectly each time.



To get is such that the minimum clearance from the edge of the platform to the edge of the cover is a half inch, you'd need 9.232" sides on the base.
 
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Wmcmanus

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You guys are absolutely awesome! Seriously, many thanks!
 
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