The
Harriss Spiral is a new discovery that deals with the golden ratio discovered
by Edmund Harriss. The golden ratio is well known and is very familiar in
everyday life, you just have to know where to look. It was used back hundreds
of years ago when the Great Pyramids where built and have been used ever since.
The golden ratio is used with rectangles and that is how the Harriss Spiral is
made. The term golden ratio in an easy sense to put it is perfection. To figure
out the golden ratio you must do a number of steps. First you must divide a
single line where one length is longer than the other. You also need to
however, get the same numbers when you divide the longer piece by the shorter,
and also the whole length of the line divided by the longer segment. When you
do this both numbers should be exactly the same. The formula for this is a/b= (a+b)/a.
Knowing this is very important in finding out how to make the Harriss Spiral.
In
addition, the Harriss Spiral is what it sounds like, a spiral. The only
difference between this and a normal spiral is that it is used with the golden
ratio. To get this however we start off with what is known as the “golden
curve.” So if you have a big rectangle that follows the guidelines of the
golden rule you can essentially put littler rectangles inside of it that can
also follow the rules. It is hard to explain this however because it is not
necessarily a rectangle inside a rectangle but rather as subdividing each
rectangle into a smaller one. To get to the “golden spiral” you draw half
circles in each of the rectangles connecting them and it will make a perfect
spiral.
Although,
the “golden spiral” and the Harriss Spiral are similar, they are not the same.
Instead of cutting the rectangles into smaller rectangles only he used two
rectangles and a square. The ratio of the first rectangle sides were 1.325.
Once you have this you keep subdividing only the rectangle into the same thing,
two rectangles and a square but smaller. You will do this for all of the
rectangles, but never for the squares. This is hard to just picture in your
head, but once you read this and see the picture it will all make since. You
are going to repeat this process four times subdividing only the rectangles.
Once you have done this you are now able to draw the “golden spiral” by drawing
quarter circles inside just the squares. Doing this however leaves out multiple
squares and this is how it is different than the “golden spiral.” 
Furthermore,
now you must draw quarter circles inside the other, smaller squares. Doing this
will allow you to have more little spirals connected to the “golden spiral.” In
the largest square that is shown the quarter circle in that shape is now
removed, giving us the Harriss Spiral. When I first thought about it, it
sounded easy like that was that all, but how he explained this is why I choose
this topic. It is not hard to make something never seen before. I totally stand
behind him with this saying because it’s really not hard to make something up.
We were all kids at one point and had our imaginary friends, or scribbled on
something and created “art.” The next thing he says however really intrigued
me. As I quote, “It is more difficult to
make something mathematically satisfying that people haven’t seen before.” It
is easy just to make something up, but to make it up that also goes along with
math is hard I believe.
However,
most discoveries made have been found before. When searching to see if anyone
has done this he found out matter of fact no one ever did. Is number that he
used for the ratio as 1.325 was used and is known as the “plastic number.”
Although this was found no one ever drew the spiral accommodated with it so he
made a new discovery. Like most discoveries you get to name it so he named it
after his last name Harriss. He has also tried to do this with different ratios
to see what he could come up with, but none similar to his first discovery, the
Harriss Spiral.
All
in all, when researching this and reading more about it, the more intrigued I
became. Just the fact that it looks like something simple but nobody ever thought
of it is neat to me. This may not like change the world in all, but it shows
how if you put your mind to something you are able to make a new discovery. The
flip side to that though is that he have to make a discovery dealing with math,
may not be something life changing, but it is a new discovery.
Bibliography
"What
Is the Golden Ratio? | LiveScience." Livescience. 2015 Purch, 24
June 2013. Web. 11 Nov. 2015.
<http://www.Livescience.com/37704-phi-golden-ratio.html>.
Meisner, Gary. "Golden Ratio
Properties, Appearances and Applications Overview." The Golden Ratio
Phi 1618. 1997-2015 PhiPoint, LLC, 12 July 2015. Web. 11 Nov. 2015.
<http://www.goldennumber.net/golden-ratio/>.
Bellos, Alex. "The Golden Ratio
Has Spawned a Beautiful New Curve: The Harriss Spiral." 2015 Guardian News
and Media Limited or Its Affiliated Companies, 13 Jan. 2015. Web. 11 Nov. 2015.
<http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/jan/13/golden-ratio-beautiful-new-curve-harriss-spiral>.
I have never heard about the Harriss Spiral or the “golden spiral” before reading this post. I understand the importance of the golden spiral and how it was used to build the pyramids and things like that but the Harriss Spiral’s purpose confuses me. I am not quite sure how it can be applied to real life scenarios. It is an interesting image to look at, but I feel like it was randomly made up. Yes, it contains mathematical properties, but it seems to have no use. I think Harriss created this spiral to have a mathematical concept named after him, but I don’t find his discovery significant. I was intrigued, however, by the concepts of the golden ratio, the golden spiral, and the golden curve. These concepts are viewed as perfect in the mathematical world which is interesting because I feel like mathematicians are always trying to find a more perfect answer. I also am curious about the “plastic number”. I am interested about it’s origin and how it allows the Harriss Spiral to work. Overall, I found this post interesting, but I would just like to know a little bit more about the Harriss Spiral and its applications.
ReplyDeleteWhen I began reading this I thought it was going to be a super simple topic that I have heard a million times before. The topic of the Golden Spiral is complex and the pictures Devin included helped me understand the message easier. However, I would agree with Molly because the Harriss Spiral only didn’t change the Golden Spiral in a significant enough way to make a difference. He only subtracted one thing from the original and therefore a “breathtaking” new discovery. It might be hard to find new things in math because it is all just numbers, but Harriss didn’t achieve anything we didn’t already know by changing the spiral.
ReplyDeleteHarriss’s Spiral is a very interesting concept in how it actually works. I’ve seen this spiral before in some online articles and youtube videos, but I never knew how it worked. I also did not know that Harriss’s Spiral was connected to the Golden Ratio in the way that it works. Dividing rectangles up into smaller and smaller rectangles then continuing the spiral through only the rectangular pieces to create a perfect spiral is very interesting to me. I find this spiral pattern to be very elegant and beautiful to look at, and now knowing how it works makes it just that much cooler of a piece of art and math.
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ReplyDeleteThough I know I have seen the harriss spiral, I never knew that there was so much math behind it or even what it was called. It’s very interesting how the rectangle is systematically broken up into pieces that create something called the golden ratio. Essentially, these rectangles can be broken down further and further into the golden ratio infinitely, but after so many times the rectangles get so small that it no longer makes sense to continue. If you draw quarter circles connecting each of the rectangles you end up with a curly pattern called the Harriss Spiral. All in all, it was a very interesting read.
ReplyDeleteI have never heard of the harries spiral before and the topic itself seems rather challenging to me.I do not understand where this topic is used. I have however heard of the golden ratio, which I had only heard of in art class. Before reading this I had never thought of this ratio as something very mathematical for some reason. I am however confused as to where in mathematics or where in other things this is used. The topic itself seems quite intriguing and I definitely learned many new things from reading this. The spiral itself is very interesting but I am confused as to why it was created in the first place.
ReplyDeleteI think it’s really cool and slightly ironic that you researched the Harriss Spiral because I came across it in my research about the Golden Ratio, and was pretty intrigued by it. I really like how it’s such a neat and clean spiral, yet it continues infinitely and is devised by the use of an irrational number. It’s also really interesting how Golden Spirals, made of connected quarters of circles, can continue infinitely when branched off of and within one another based on the subdivision of more and more squares. Although doing this leaves out multiple squares, I find it noteworthy that someone could devise something like this by most likely just playing around with the spirals, but with at least a bit of a method to the madness.
ReplyDeleteDevin’s post on Harriss Spirals was very cool. I liked how they tied into the Golden Ratio, like Monica talked about in her post, but they were also pleasing to the eye. I found the minute differences between the golden spiral and the Harriss spiral to be a tad bit confusing. I think that if the pictures of the two had been side by side, or if the pictures were labeled better in the post, that it would clear up the differences between them. I liked how Devin touched on how though this may not be a world-altering discovery, but it is cool that someone was interested in it enough to puzzle it out.
ReplyDeleteI never knew there was such thing as a Harriss Spiral. I only knew of the golden ratio but I see they are very similar in formation but the Harriss Spiral doesn't continue a trend of growing or shrinking rectangles. Instead I see sub divisions of the rectangle that creates many spirals all on one structure. Using this spiral, it looks like you could create some really interesting abstract art. The Harris Spiral is just more proof of how prominent the golden ratio is to nature, math, art, and many other things. I wonder if the Harriss Spiral is found anywhere in nature?
ReplyDeleteI found the Harris Spiral confusing and a bit unimportant because of the lack of real world applicability to it. It is hard to understand the purpose of it other than being something new and undiscovered before. I found the equation of how to get the Harris Spiral is complicated as well. I did find it interesting that it tied into the Golden Ratio and was composed of dividing rectangles into smaller rectangles and so on. Overall, it think the Harris Spiral is a personal accomplishment for it’s discoverer, but has little value when advancing mathematics as a whole and solving any unanswered questions or bringing forth new ones.
ReplyDeleteBefore reading this I never knew what the Harris Spiral was called. I had seen it before reading this but I never took the time to learn about it. One thing I like about this topic is how directly related it is to the golden ratio. That has always been a topic to catch my eye. After reading this though I was still a little bit confused on how the Harris Spiral was constructed. I agree with what Ryan said that when it comes down to it, the Harris Spiral is a cool personal discovery but does not do much to advance mathematics.
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