Thread: Need some geometry help

Big ask for a formula Waveink. It is very difficult to see whether that is a repeating pattern.If it is it may not be such a problem.

I also think that each part of that web is cut from a globe, so the curve is already there.

However it is a challenge so I will mess about with it.

trial and error

Forget maths use soccer ball pumped up hard and work from that make enough paper pieces to create 1/2 of it double the amount plus 5 easy

I think I've figured it out bro....
Give me about 2 hr, I've managed to get it draw on AchiCAD, now just need to edit & hopefuly can post it here.

It's like a puzzle that constructed from many "stars". The key shape to start with is a PENTAGONAL shape constructed from 5 of the "stars".

The tricky part is how to arrange the set.
The good news is, I finally figure it out.

Tried the soccer ball method, but every time I cut a hole in it the ball goes flat.

The patterns look irregular. Is it important to replicate this picture exactly? If not, I would settle on a pentagon about the right size. Cut out a lot of these. Paste them around a ball of about the right size, matching where you would put the pins through. This will lead you to a final shape to close the ball which may or may not be regular. Cut a pattern for this final shape, and use that particular one as the hold where the wire goes in at the top. There probably is a neat geometric solution somewhere but I think my method would work, although it would produce a more regular pattern than the one in the picture.

Patterns like this are generally based on subdivisions of the facets of "simple" polyhedra, such as icosahedrons. The subdivision intersections are then projected to the surface of the circumscribing sphere. Facets are usually equilateral triangles, and so are the subdivisions. Because of the sphere's curvature, the projected spherical triangles are usually not identical.

In this case, however, I think it can be made of identical star-like components. Draw two equilateral triangles joined along a base line. For work points, use the midpoints of one triangle, and the end points of its neighbour. I'm not sure how many are needed, or what "simple" polyhedron is the basis; probably something weird such as a rhombic dodecahedron, and maybe two of them overlapping.

There are formulas for relations amongst components of spherical triangles under the subject of Spherical Trigonometry. And graphical solutions can be found via Descriptive Geometry. CAD of some sort makes it easier, and more precise. (After you wrap your brain around it.)

Cheers,
Joe

Hi... saw your post ... not sure if this helps..
Your making a globe-shape... obvious 360 degress.... half the globe... now were at 180.... so how many joins over half the sphere... couldn't the angle of each join be calculate in that fashion...???
Just trying to use logic to help...
Hope this doesn't sound stupid.
Kerry

Ok I started working this out based on the size of the lamp and the fact that the shapes are all the same, one side of the shape has 3 legs the other side has 2. Now this results in you having 2 triangles in the shape and they are right angled triangles. Now acording to Pythagorus the square on the hypotenuse is equal to the sum of the squares on the other two sides. This I know because it was the maths teachers pet punishment (Write out 200 times neatly in ink). Anyways after getting all that info, I came to the conclusion based on the size of the globe and the inability to think straight any more that your shape was about 10CM X12CM give or take. The shape though does have an issue, to get a standard globe into it if all segments are fixed you need about a span of 14cm which is too big.

Originally Posted by hcim

I think I've figured it out bro....
Give me about 2 hr, I've managed to get it draw on AchiCAD, now just need to edit & hopefuly can post it here.

It's like a puzzle that constructed from many "stars". The key shape to start with is a PENTAGONAL shape constructed from 5 of the "stars".

The tricky part is how to arrange the set.
The good news is, I finally figure it out.
http://img219.imageshack.us/img219/8...etrymchcop.jpg

Here is the detail on how I figure it out:

The whole globe consist of many small identical "star look" shape that are jointed in a certain pattern/interval. At glance it may look irregularly joint.
If you look closely, you should easily spot a Pentagonal shape when 5 of the stars are jointed on their longest leg.
Therefore, there are two key geometrical shape that you need to concentrate on as reference, i.e. :

1. Star shape
2. Pentagonal shape

Step I. STAR shape dimensions

The easiest way to figure out the STAR dimension is by drawing a pentagonal shape and find its center point.
--- See Illustrated Picture 1 ---




From above illustration we can derived the detail dimension of the STAR shape component. As in the following picture:





Step II. STAR Shape Arrangement

To assembly the STARs in order to construct the globe, we need to figure out how each legs should be joint together in certain arrangement.
Let's assume the following terminology (should we say the STAR anatomy).

The STAR consist of :

• 1 long leg (which is 1.376 longer than the short legs)
• 4 short legs of the same length, and 60 degree apart.
• +
• There are 2 Side Opening (mirrored left and right)
• and 1 Bottom Opening (which is the opposite of the longest leg)

The arrangement is easier by start joining 5 STAR on their longest leg, so that they form a Pentagonal shape pattern.

Then here is coming the tricky part, joining the side and bottom opening.
In doing this, we should carefully joint the 2 Side Opening so that one is connecting to other STAR Side Opening and the other Side Opening to other STAR Side Opening.
Hint : Notice that the longest leg on the other 2 STARS SHOULD pointing toward different directions. If they are pointing on different direction BUT is a mirror to each other, then it's not right !!



HOWEVER, in 2D drawing, it's not possible to perfectly joint them so that each legs is intercepting to each other.
Luckily we're making a sphere shape. In the real assembly, when you joint those gaps, the the whole assembly should curved and gradually forming a sphere, i.e the globe shape.

Hopefully these will give you something to start with, instead of trial and error. .

Thx,
Mich

I think that if you look for how to build a Geodesic Dome you'll find many calculators for the angles and such. Just put each half together to make your sphere.

One stupid question...

If you build the lamp into the sphere, how are you going to change the light (CFL etc.) bulb?

Many thanks to all and sundry for your help - I laughed out loud with the picture of Wongdai cutting a hole in his soccer ball.

Obviously hcim, you have way too much time on your hands, and way too many brain cells left still firing. Your explanation was spectacular - and exactly what I needed. Many thanks.

Oh and rrich - who said I'm changing the globe - the lady wants it, the lady can change the globe! Will be almost as much fun watching her figure that out as watching Wongdai cutting his soccer ball!

Thanks again folks.

I think it is a variation on a buckyball. This might help:


http://199.6.131.12/en/scictr/lab/buckyball/index.htm

Very impressed HCIM. Great stuff.

I reckon if you make one of the stars removable, you should be able to pull a bulb through that to change it.

Tex

Awesome work HCIM.