I'm sorry, but I don't have a picture for this problem. I hope I can
describe it clearly.
Suppose you have two cubes, one 3" on a side, and the other slightly
larger, say like 3.1" on a side.
The problem is to drill a hole through the SMALLER cube such that the
larger cube can pass through the smaller cube, through the hole.
If you take the smaller cube and hold it between your index finger and
thumb, holding it at opposite vertices (the major diagonal of the cube),
you can see but twirling the cube to the right angle that from this
perspective, it's cross-section is a hexagon.
It just happens that the hexagonal cross-section of a 3" cube is in fact
large enough to drill a square hole through it that would pass a 3.1"
square.
So my problem ... HOW do I possibly construct this beast? What I need
to do is take a cube and drill a hole through it at this strange angle.
Then I need to "square" the hole, making it clean enough to let the
larger cube pass through it.
It's a really neat math construct that is great to show to high school
kids. Anyone have any ideas how I would approach making this?
Jack
Cheater <grin>
"Mike Richardson" <[email protected]> wrote in message
news:y%[email protected]...
> At this web site:
> http://yucs.org/~gnivasch/cube/index.html
>
> You will see all the cuts laid out to create the construct.
>
> Regards
> Mike
>
> "mywebaccts (at) PLUGcomcast.net" <"mywebaccts (at) PLUGcomcast.net">
> wrote in message news:[email protected]...
>> I'm sorry, but I don't have a picture for this problem. I hope I can
>> describe it clearly.
>>
>> Suppose you have two cubes, one 3" on a side, and the other slightly
>> larger, say like 3.1" on a side.
>>
>> The problem is to drill a hole through the SMALLER cube such that the
>> larger cube can pass through the smaller cube, through the hole.
>>
>> If you take the smaller cube and hold it between your index finger and
>> thumb, holding it at opposite vertices (the major diagonal of the cube),
>> you can see but twirling the cube to the right angle that from this
>> perspective, it's cross-section is a hexagon.
>>
>> It just happens that the hexagonal cross-section of a 3" cube is in fact
>> large enough to drill a square hole through it that would pass a 3.1"
>> square.
>>
>> So my problem ... HOW do I possibly construct this beast? What I need to
>> do is take a cube and drill a hole through it at this strange angle. Then
>> I need to "square" the hole, making it clean enough to let the larger
>> cube pass through it.
>>
>> It's a really neat math construct that is great to show to high school
>> kids. Anyone have any ideas how I would approach making this?
>>
>> Jack
>>
>
>
Thanks again to everyone for their help. I'll probably "cheat" with the
paper model first, if not only to help better visualize the final
product. Then I think I'll try a jig approach. I don't know anyone
with a mill and I'm not looking for a 'perfect' rendition, just one good
enough to help confound and convince the kids of the beauty of math!
Jack
mywebaccts (at) PLUGcomcast.net wrote:
> I'm sorry, but I don't have a picture for this problem. I hope I can
> describe it clearly.
>
> Suppose you have two cubes, one 3" on a side, and the other slightly
> larger, say like 3.1" on a side.
>
> The problem is to drill a hole through the SMALLER cube such that the
> larger cube can pass through the smaller cube, through the hole.
>
> If you take the smaller cube and hold it between your index finger and
> thumb, holding it at opposite vertices (the major diagonal of the cube),
> you can see but twirling the cube to the right angle that from this
> perspective, it's cross-section is a hexagon.
>
> It just happens that the hexagonal cross-section of a 3" cube is in fact
> large enough to drill a square hole through it that would pass a 3.1"
> square.
>
> So my problem ... HOW do I possibly construct this beast? What I need
> to do is take a cube and drill a hole through it at this strange angle.
> Then I need to "square" the hole, making it clean enough to let the
> larger cube pass through it.
>
> It's a really neat math construct that is great to show to high school
> kids. Anyone have any ideas how I would approach making this?
>
> Jack
>
> Suppose you have two cubes, one 3" on a side, and the other slightly
> larger, say like 3.1" on a side.
>
> The problem is to drill a hole through the SMALLER cube such that the
> larger cube can pass through the smaller cube, through the hole.
>
> If you take the smaller cube and hold it between your index finger and
> thumb, holding it at opposite vertices (the major diagonal of the cube),
> you can see but twirling the cube to the right angle that from this
> perspective, it's cross-section is a hexagon.
>
> It just happens that the hexagonal cross-section of a 3" cube is in fact
> large enough to drill a square hole through it that would pass a 3.1"
> square.
>
> So my problem ... HOW do I possibly construct this beast? What I need to
> do is take a cube and drill a hole through it at this strange angle. Then
> I need to "square" the hole, making it clean enough to let the larger cube
> pass through it.
>
> It's a really neat math construct that is great to show to high school
> kids. Anyone have any ideas how I would approach making this?
Don't start with a cube; start with stock that's much larger and drill out
the hole first. Then slice off the stock that is beyond the boundaries of
the cube. Just take care that you orient the hole, or your cuts,
appropriately. What's left is your finished cube.
- Owen -
"mywebaccts (at) PLUGcomcast.net" <"mywebaccts (at) PLUGcomcast.net"> wrote
in message news:[email protected]...
> So my problem ... HOW do I possibly construct this beast? What I need to
> do is take a cube and drill a hole through it at this strange angle. Then
> I need to "square" the hole, making it clean enough to let the larger cube
> pass through it.
Another technique is to build your cube around the hole.
I.e.
Make a cube which is very slightly larger than your 3.1 inch cube. This
cube
will define the size of the hole. Thus it is slightly larger to allow a
little clearance.
Wax the outside of this cube so that glue will not stick to it.
Build a larger cube around the first cube. (The size of this cube is left as
an
exercise for the reader.) I would build this cube by gluing several pieces
of wood together around the first cube.
You now have a cube inside of a cube.
Now rotate the pair of cubes and slice off the corners to create a 3 inch
cube.
(The design of this jig is another exercise for the reader.)
When you are done you will have both your desired cube with its hole
and also a piece which represents the shape of the hole that was cut
out of the cube. Since it sounds like you want something to demonstrate
the principles involved, having both pieces would be useful.
That is some impressive googling man.
-Steve
"Mike Richardson" <[email protected]> wrote in message
news:y%[email protected]...
> At this web site:
> http://yucs.org/~gnivasch/cube/index.html
>
> You will see all the cuts laid out to create the construct.
>
> Regards
> Mike
>
> "mywebaccts (at) PLUGcomcast.net" <"mywebaccts (at) PLUGcomcast.net">
> wrote in message news:[email protected]...
>> I'm sorry, but I don't have a picture for this problem. I hope I can
>> describe it clearly.
>>
>> Suppose you have two cubes, one 3" on a side, and the other slightly
>> larger, say like 3.1" on a side.
>>
>> The problem is to drill a hole through the SMALLER cube such that the
>> larger cube can pass through the smaller cube, through the hole.
>>
>> If you take the smaller cube and hold it between your index finger and
>> thumb, holding it at opposite vertices (the major diagonal of the cube),
>> you can see but twirling the cube to the right angle that from this
>> perspective, it's cross-section is a hexagon.
>>
>> It just happens that the hexagonal cross-section of a 3" cube is in fact
>> large enough to drill a square hole through it that would pass a 3.1"
>> square.
>>
>> So my problem ... HOW do I possibly construct this beast? What I need to
>> do is take a cube and drill a hole through it at this strange angle. Then
>> I need to "square" the hole, making it clean enough to let the larger
>> cube pass through it.
>>
>> It's a really neat math construct that is great to show to high school
>> kids. Anyone have any ideas how I would approach making this?
>>
>> Jack
>>
>
>
Yeah, what Owen said.
-Zz
On Thu, 29 Jun 2006 22:41:20 -0400, "Owen Lawrence"
<[email protected]> wrote:
>> Suppose you have two cubes, one 3" on a side, and the other slightly
>> larger, say like 3.1" on a side.
>>
>> The problem is to drill a hole through the SMALLER cube such that the
>> larger cube can pass through the smaller cube, through the hole.
>>
>> If you take the smaller cube and hold it between your index finger and
>> thumb, holding it at opposite vertices (the major diagonal of the cube),
>> you can see but twirling the cube to the right angle that from this
>> perspective, it's cross-section is a hexagon.
>>
>> It just happens that the hexagonal cross-section of a 3" cube is in fact
>> large enough to drill a square hole through it that would pass a 3.1"
>> square.
>>
>> So my problem ... HOW do I possibly construct this beast? What I need to
>> do is take a cube and drill a hole through it at this strange angle. Then
>> I need to "square" the hole, making it clean enough to let the larger cube
>> pass through it.
>>
>> It's a really neat math construct that is great to show to high school
>> kids. Anyone have any ideas how I would approach making this?
>
>Don't start with a cube; start with stock that's much larger and drill out
>the hole first. Then slice off the stock that is beyond the boundaries of
>the cube. Just take care that you orient the hole, or your cuts,
>appropriately. What's left is your finished cube.
>
> - Owen -
>
On Thu, 29 Jun 2006 16:22:32 -0600, "mywebaccts (at) PLUGcomcast.net"
<"mywebaccts (at) PLUGcomcast.net"> wrote:
>I'm sorry, but I don't have a picture for this problem. I hope I can
>describe it clearly.
>
>Suppose you have two cubes, one 3" on a side, and the other slightly
>larger, say like 3.1" on a side.
>
>The problem is to drill a hole through the SMALLER cube such that the
>larger cube can pass through the smaller cube, through the hole.
>
>If you take the smaller cube and hold it between your index finger and
>thumb, holding it at opposite vertices (the major diagonal of the cube),
>you can see but twirling the cube to the right angle that from this
>perspective, it's cross-section is a hexagon.
>
>It just happens that the hexagonal cross-section of a 3" cube is in fact
>large enough to drill a square hole through it that would pass a 3.1"
>square.
>
>So my problem ... HOW do I possibly construct this beast? What I need
>to do is take a cube and drill a hole through it at this strange angle.
>Then I need to "square" the hole, making it clean enough to let the
>larger cube pass through it.
It should not be difficult to jig this for a drill press/morticer.
Build an angled auxillary table at the "strange angle", which if
you're teaching this I hope you know what it is ;) Then attach
another piece with a 90 degree notch but at 45 degrees to hold the
cube in place. That will let you drill a hole. You can use the same
setup to hold the cube while you hold your chisel vertically.
I agree with the other poster though, it'd be easier to assemble it
out of 6 precut sides, but not as nice of a visual aid.
-Leuf
On Thu, 29 Jun 2006 16:22:32 -0600, "mywebaccts (at) PLUGcomcast.net"
<"mywebaccts (at) PLUGcomcast.net"> wrote:
>The problem is to drill a hole through the SMALLER cube such that the
>larger cube can pass through the smaller cube, through the hole.
You can't drill this, you have to bore it.
A "drill" is a self-guided tool for cutting holes. "Boring" (in workshop
terms) is a different process - you clamp it rigidly to a rigid machine,
then you rotate a single point cutter so as to cut the hole. The
difference is that the tool is guided by the rigidity of the frame and
machine, not a rubbing contact on the tool.
Find someone with a milling machine (most engineering workshops), make
up a 3-pointed stand to support it and away you go.
Yeah, what Andy said.
-Zz
On Fri, 30 Jun 2006 18:32:31 +0100, Andy Dingley
<[email protected]> wrote:
>On Thu, 29 Jun 2006 16:22:32 -0600, "mywebaccts (at) PLUGcomcast.net"
><"mywebaccts (at) PLUGcomcast.net"> wrote:
>
>>The problem is to drill a hole through the SMALLER cube such that the
>>larger cube can pass through the smaller cube, through the hole.
>
>You can't drill this, you have to bore it.
>
>A "drill" is a self-guided tool for cutting holes. "Boring" (in workshop
>terms) is a different process - you clamp it rigidly to a rigid machine,
>then you rotate a single point cutter so as to cut the hole. The
>difference is that the tool is guided by the rigidity of the frame and
>machine, not a rubbing contact on the tool.
>
>Find someone with a milling machine (most engineering workshops), make
>up a 3-pointed stand to support it and away you go.
Sounds like an interesting project. My approach (simplistic ) would be:
Layout six flat pieces of wood sized appropriately
Make your straight saw cuts with whatever - a jigsaw, etc
glue the six sides into a cube
Toughest part is laying out the drawing on the flat wood( or whatever)
stock.
HTH,
Vic
"mywebaccts (at) PLUGcomcast.net" <"mywebaccts (at) PLUGcomcast.net"> wrote
in message news:[email protected]...
> I'm sorry, but I don't have a picture for this problem. I hope I can
> describe it clearly.
>
> Suppose you have two cubes, one 3" on a side, and the other slightly
> larger, say like 3.1" on a side.
>
> The problem is to drill a hole through the SMALLER cube such that the
> larger cube can pass through the smaller cube, through the hole.
>
> If you take the smaller cube and hold it between your index finger and
> thumb, holding it at opposite vertices (the major diagonal of the cube),
> you can see but twirling the cube to the right angle that from this
> perspective, it's cross-section is a hexagon.
>
> It just happens that the hexagonal cross-section of a 3" cube is in fact
> large enough to drill a square hole through it that would pass a 3.1"
> square.
>
> So my problem ... HOW do I possibly construct this beast? What I need to
> do is take a cube and drill a hole through it at this strange angle. Then
> I need to "square" the hole, making it clean enough to let the larger cube
> pass through it.
>
> It's a really neat math construct that is great to show to high school
> kids. Anyone have any ideas how I would approach making this?
>
> Jack
>
At this web site:
http://yucs.org/~gnivasch/cube/index.html
You will see all the cuts laid out to create the construct.
Regards
Mike
"mywebaccts (at) PLUGcomcast.net" <"mywebaccts (at) PLUGcomcast.net"> wrote
in message news:[email protected]...
> I'm sorry, but I don't have a picture for this problem. I hope I can
> describe it clearly.
>
> Suppose you have two cubes, one 3" on a side, and the other slightly
> larger, say like 3.1" on a side.
>
> The problem is to drill a hole through the SMALLER cube such that the
> larger cube can pass through the smaller cube, through the hole.
>
> If you take the smaller cube and hold it between your index finger and
> thumb, holding it at opposite vertices (the major diagonal of the cube),
> you can see but twirling the cube to the right angle that from this
> perspective, it's cross-section is a hexagon.
>
> It just happens that the hexagonal cross-section of a 3" cube is in fact
> large enough to drill a square hole through it that would pass a 3.1"
> square.
>
> So my problem ... HOW do I possibly construct this beast? What I need to
> do is take a cube and drill a hole through it at this strange angle. Then
> I need to "square" the hole, making it clean enough to let the larger cube
> pass through it.
>
> It's a really neat math construct that is great to show to high school
> kids. Anyone have any ideas how I would approach making this?
>
> Jack
>