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Kaleidoscope Review V2N2

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a short issue but a good one. It talks about the golden ratio and golden angle and how they are applied to kaleidoscopes! More on these subjects to come in future issues. Hopefully I will produce them more often.
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    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 couldn’t 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 Tickle’s 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 scope’s 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 don’t 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 HIS IS A SHORT ISSUE   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! his issue was kindly printed out for you by the person or business  who’s  return address is below. Be sure to thank them for doing so and remind them to include you in all future issues. If someone didn ’ t 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.
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