The Incredible New Kaleidoscope Eclectic Review page 1

KALEIDOSCOPE

ECLECTIC REVIEW Volume 2, Issue 2

Copyright 1999, 2013-2014 B. Bensley

The Incredible New Kaleidoscope Eclectic Review page 2

Welcome to The Incredible

New Kaleidoscope Eclectic

Review! By Brett Bensley, Editor

Why the new name? I just couldnt keep things

constant. Everything grows and matures, or at least it

should.

When I first started this magazine, it was called

Kaleidoscope Review. This was appropriate for its

purpose at the time. I would review kaleidoscopes,

artists, stores, and more in each issue. I would still do

that if some of you would send in materials, pictures, or

items for the reviews. SEND THEM IN!

After a number of years of being absent, I restarted the

magazine in its current form and changed the name to

differentiate it from the past issues. Thus is became

The New Kaleidoscope Review. This suited its needs

and purpose.

I would send our emails and notices that The New

Kaleidoscope Review was available and used the initials

in the correspondence: TNKR. Every time I read that,

my mind added I and E making it TINKER. I

thought this was appropriate as well. So I pondered

about the two additional words to make it TINKER.

Incredible as it seemed, Incredible was an easy choice.

It fit nicely within The New. But finding the E word

was a challenge. Eclectic came to me out of the blue

after searching for all the positive E words. Eclectic

seemed very appropriate for the E word to change the

initials to TINKER. And it seemed that was the way

this magazine seemed to be heading anyway. So

Eclectic, deriving ideas, style, or taste from a broad

and diverse range of sources, is the appropriate word

to describe this magazine. The other definition, of,

denoting, or belonging to a class of ancient

philosophers who did not belong to or found any

recognized school of thought but selected such

doctrines as they wished from various schools, is

more about me and my ideas as regarding

kaleidoscopes and the kaleidoscope world.

Enough about the new name. Enjoy this issue and all

future issues!

Fibonacci and the Golden Angle For those that have math anxiety, I recommend you

put this down and read one of the other issues

available.

When we discuss Fibonacci, we will not be discussing

Marc Tickles kaleidoscope. We will be talking about

the golden ratio and the golden angle.

What is the golden ratio?

The golden ratio exists if the ratio between two values

is the same as the ratio of the sum of the two values to

the larger of the two values.

Or if (a + b)/a = a/b.

Fibonacci is involved because the ratio of the Fibonacci

sequence approaches the golden ratio.

To simplify, this ratio makes the object more attractive

to the viewer. There are many noted references

mentioning this ratio on the internet these days.

Ancient Greeks used it in their architecture.

What does this have to do with kaleidoscopes?

I am suggesting that the height of the scopes diameter

to length use this ratio. Though we have to use

discretion, if our kaleidoscope is eight inches long, then

the diameter might be more pleasing at about three

inches.

Check around your collection of scopes. See how

many might be approaching this general shape and how

they affect you. Personally, I like the way these look on

a shelf or in the hand. If they get too long, or too short

and stubby, they just dont look as nice, but are still

attractive.

I am not recommending this as a rule, because as all

well know, I do not follow this in my scopes, but have

on some of my more popular selling scopes.

You may include the turning chamber in this ratio as

part of your design. In our previous case, I would have

an eight inch long kaleidoscope body with a three inch

diameter and the turning part holding the object case

would also be about three inches of the total eight inch

body length.

The Incredible New Kaleidoscope Eclectic Review page 3

There are many web pages dedicated to the wonderful

golden ratio, and I recommend you take some time to

view a few.

But the golden ratio is applied to circular images as

well. Where do we kaleidoscope lovers and artists find

such a circular image? Inside the kaleidoscope.

I will get down to the simple detail here, the optimum

angle making the golden angle is about 137.508.

Although making a kaleidoscope with the mirrors at

137.508 degrees between them is not optimum, those

angles that combine to make up an almost 137.508

degrees will be most pleasant.

As you can see to the table to the right, we can see that

a number of our perfect kaleidoscope angles will be

close to the golden angle when added.

One of my favorites is the 45 degree mirror system,

and guess where that ends up:

137.508/45 = 3.05573

Here I am dividing the 137.508 by the 45 degrees to get

the number of times. I could have divided the 137.508

by the three to get what the angle should be.

My 45 degree angle is very close to fitting nicely, three

times, in the 137.508 degree golden angle!

Let us try another:

137.508/6 = 22.918

This is close to the 22.5 degrees for a 16 point

reflection kaleidoscope!

As you continue to decrease the degrees and increase

the reflections, the more frequent it gets close or

matches the golden angle. Could this be why the 180,

90, and 60 degree mirror systems are not as liked or as

popular as those that are very close to the golden angle?

My suggestions are that you can design a kaleidoscope

that takes advantage of this proven (in other fields)

concept and apply it to your kaleidoscope artistry.

Check your scopes that you either make or buy and see

how well it matches the golden angle and the golden

ratio.

degree (n) Reflections =

360/n

180 2

90 4

60 6

45 8

36 10

30 12

25.71 14

22.5 16

20 18

18 20

16.36 22

15 24

13.85 26

12.86 28

12 30

11.25 32

10.59 34

10 36

9.47 38

9 40

8.57 42

8.18 44

7.83 46

7.5 48

7.2 50

The Incredible New Kaleidoscope Eclectic Review page 4

T H I S I S A S H O R T I S S U E

I am sorry for keeping this short, but I am working on

a future issue to continue this subject and more.

There are so many planned projects that I wanted to

keep your interest. Next issue, I hope, will be a

construction issue with a project for the golden ratio

and one for kaleidoscope building. I also have planned

some kind of competition for kaleidoscope artists. I

am working on the details for this to make it fair, but

enjoyable for all.

Above all, please email me with ideas, pictures, concept

for future issues of The Incredible New Kaleidoscope

Eclectic Review (TINKER).

Also, visit our facebook page:

Search for The New Kaleidoscope Review

And join!

This issue was kindly printed out for you by the person or business whos return address is below. Be sure to thank them for doing so and remind them to include you in all future issues. If someone didnt print this out and mail this to you, then you can do so for others. It is great to pass this on to all interested in kaleidoscopes.