>

Ciao Samuele

> Ciao a tutti,

> mi chiamo Samuele ed è già da un pò di tempo che sono iscritto, scusami se non sono una

> parte attiva di questa mailing list ma vi dovrei chiedere un grosso favore.

> Tempo fa andai nel sito di Rosalinda Sanchez

> (http://members.aol.com/rrosalinda/rosa.html) in cui ci sono delle bellissime foto,

> specialmente quelle dei modulari, specialmente quelle del modulare Orb di Jeannine

> Mosley. ...

Tempo fa avevo scritto a Rosalinda proprio per gli orbs, e lei (gentilissima)

mi aveva mandato le istruzioni (ascii) che giravano. Non so se ne

esistano altre, comunque eccole qui. Sono 3 mail di Jeannine. Le ho

incluse nella mia mail, spero non vengano tagliate da Yahoo.

Buone pieghe

Roberto

====================================================

Date: 4/6/1997 22:21

From: j9@... (Jeannine Mosely)

Subject: spherical model

I have been playing with variations on the following model for the

last month. I hope you all will enjoy it. I am indebted to Paul

Jackson for the inspiration that led to its discovery.

Using a square of stiff paper or light card stock, 3-5 inches across,

score four half circlular arcs on the paper, each with a radius that

is one fourth the length of the square's diagonal, one centered on

each of the square's four edges. Each arc will just touch the two

arcs on either side of it. Mountain fold the scored lines, rolling

each of the half-circles gently into a partial cone. The paper will

somewhat resemble a balloon base. In the same way that six balloon

bases can be assembled into a sort of skeletal octahedron, six of

these go together to make a ball with eight conical dimples. If you

are not familiar with the ballon base model, it works by alternating

slipping the point of one module inside or outside the point of an

adjacent module.

-----------------------

| | | |

|... . . ...|

| .. .. .. .. |

| . ..... . |

| . . |

| . . |

| . . |

| . . |

| .. ..... .. |

|... .. .. ...|

| . . |

| | | |

-----------------------

There are a number of related models that can be made with the

symmetries of other polyhedra. And of course, this model can be

easily modified to be made out of ... business cards!

The mathematics of this model are fairly interesting. There is some

cheating go on, in that, for the model to exist in a mathematically

pure form, the arcs that must be drawn are not true circles, but are

curves of a rather complex equation that turns out to differ from a

true circle at its worst point by less than 2 percent. If you really

want to know the truth, I can post more details.

-- Jeannine Mosely

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Date: 4/7/1997 13:40

From: j9@... (Jeannine Mosely)

Subject: tips for making the spherical model

Body:

I got some private email questions about my spherical model, and I

thought I'd answer to the list, since others might find this

information useful.

If you're in the states, buy a pack of multi-colored 4"x6" index cards

at your local office supply. If you can't get these, look for the

nearest local equivalent. Use three colors, two of each, placing

modules of the same color opposite each other.

Get as good a compass as you can afford from a drafting store. Get the

kind that holds small pieces of lead (really graphite), not the kind

that holds a pencil. These sometimes come with an extra point that

can be inserted instead of a lead. Mine did, but I bought it a long

time ago and I lost it. So I found a nail of the right diameter, cut

off the tip at a useable length and put it in the compass. The end of

the nail was pretty rough and it tore up the paper, so I filed it down

a little. (Well, I actually, I ground it with my Dremel tool, but a

file works and is more universally available.)

If you can't afford or find a good compass, you can still use the

cheap kind that holds a pencil. Get a dowel the diameter of a pencil.

Cut off a short length of it and sharpen it in a pencil sharpener. It

won't score the paper very well, but it should leave enough of an

indentation that you should be able to see it and go over it with some

other sharper tool. Scoring tools have been discussed on this list

lately, so I won't go into that here.

Alternatively, you could find something circular to trace around. The

world abounds in these, but probably none of them are just the right

diameter for the square you will be working with. So, figure out what

the right size square is for the circle you are tracing, and adjust

your square. The side of the square should be sqrt(2) = 1.414 times

the diameter of your circle.

-- Jeannine Mosely

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There are two different ways to make the six piece orb, one starting from

squares, the other from rectangles. The diagrams that I posted to this

list described only the square version. The rectangular version

generalizes to more complex orbs with more pieces and more dimples. Here's

how it works.

For the six pices rectangular orb, start with a business card or any

rectangle whose length is more than 1.5 times the width and less than 1.9

times the width. (These numbers are approximate and based on the physical

properties of the paper rather than any inherent mathematical requirement.)

"Draw" a square centered in the middle of the rectangle whose side is the

width of the rectangle. With a compass, score four circles on the card so

that each is centered at a corner of the square and whose radius is half

the width. This will cause the circles to just touch their neighbor

circles on each side. (Mathematicians call this "osculating", a fancy word

for kissing.) Curl the semi-circles into cones using the scored creases.

Assemble these in more or less the same way as for the square-based orb,

but note that each unit has just two flaps (not four) and that all flaps

are tucked to the inside of the model.

To generalize this procedure, instead of drawing a square in the center of

the rectangle, draw a rhombus. (Two of its edges lie on the long edges of

the rectangle.) Then score four circles centered at the corners of the

rhombus and just touching each of their neighbors. If you are making the

twelve piece model with fourteen dimples, the diagonals of the rhombus

should be in the ratio sqrt(2):1 and the radii of the circles should also

be in that ratio, with the small circles centered at the vertices where the

angle is obtuse and the large circles centered at the acute vertices. For

the thirty piece model with thirty two dimples, the diagonals and radii

should be in the "golden" ratio. Assemble in much the same as for the

other orbs with all flaps inside. The small radius dimples will be made up

of three obtuse angle partial cones, and the large radius dimples will be

made of four or five, depending on whether you are making the twelve or

thirty unit version.

While I do have methods of constructing these proportions, I don't have

time to describe them here. If you can't figure it out any other way, use

a calculator and a ruler.

Please note that these propotions may not be the only ones that will work.

I am still investigating the mathematics of this model.

-- Jeannine Mosely