essays on the golden rectangle

Golden Ratio Length: 538 words (1.5 double-spaced pages) Rating: Red (FREE)   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - What is the Golden Ratio The golden ration can occur anywhere. The golden proportion is the ratio of the shorter length to the longer length which equals the ratio of the longer length to the sum of both lengths. The golden ratio is a term used to describe proportioning in a piece. In a work of art or architecture, if one maintained a ratio of small elements to larger elements that was the same as the ratio of larger elements to the whole, the end result was pleasing to the eye. The ratio for length to width of rectangles is 1.61803398874989484820. The numeric value is called “phi”. The Golden Ratio is also known as the golden rectangle. The Golden Rectangle has the property that when a square is removed a smaller rectangle of the same shape remains, a smaller square can be removed and so on, resulting in a spiral pattern. The Golden Rectangle is a unique and important shape in mathematics. The Golden Rectangle appears in nature, music, and is often used in art and architecture. Some thing special about the golden rectangle is that the length to the width equals approximately 1.618      Golden Ration = Length = 1.6                 Width The golden rectangle has been discovered and used since ancient times. Our human eye perceives the golden rectangle as a beautiful geometric form. The symbol for the Golden Ratio is the Greek letter Phi. The Fibonacci Series was discovered around 1200 A.D. Leonardo Fibonacci discovered the unusual properties of the numeric series, that’s how it was named. It is not proven that Fibonacci even noticed the connection between the Golden Ratio meaning and Phi. The Renaissance used the Golden Mean and Phi in their sculptures and paintings to achieve vast amounts balance and beauty. The Golden.
Published: 23, March 2015 Some aspects of mathematics can be dull and tedious from start to end, much of it however is intriguing and inspiring, when you truly see the beauty and the relevance. This is why I would like to bring to your attention the magic of the Fibonacci numbers. If you have ever looked at a sheet of paper and wondered Why do we use those dimensions? or looked at the leaf or an attractive plant and wondered Why can I never find a four leaved clover? then this may be of some interest. Many of these things are quite interconnected in a way you would not realise, and most of them are connected by the Fibonacci sequence. If I return to one of my original questions Why can I never find a four leaved clover? it seems reasonable, that if you can find 3 leaved clover and 5 leaved clover, you would be able to find the more symmetrical 4 leaved clover. Why then is it so rare to find one? If we look closely at other examples of nature, we can perhaps find the answer. If you were to search through your average garden, you would find the majority of flowers have 5 petals, many have 3 or 8 or more but if you look closely, you will always find more of certain numbers, compared to others. These numbers just so happen to be part of the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89. Although, why does nature choose these numbers over others? In addition, the connection between the real world and this sequence does not just end there; it can be found almost everywhere we look: spirals on a snail shell, the core of an apple, geometry, art, architecture, the stock market and even the human body. So what makes it so useful? Why is it so special? My project intends to answer these questions and along the way discover new applications and more examples. I will be delving into the mathematical concepts behind the nature we see every day, the regular objects we.
Out of all of the infinite numbers in the world, there are precious few that are given their own letter from the all-too-finite Greek alphabet. The golden ratio, also known by the letter φ, or phi (usually pronounced “fie” in English), is one of those few. An irrational number that begins 1.618 , it describes an important kind of geometrical proportion—specifically, an elegant way to divide a line segment. Imagine we divide a segment (a) into a longer part (b) and a shorter part (c). If the ratio of a to b is the same as b to c, then that single ratio is golden. A rectangle whose sides are lengths a and b is called a golden rectangle, and it’s found in the geometry of a regular pentagon and the Platonic solids, five fundamental 3-D shapes, including the cube. The golden ratio is also tightly connected with the mathematically important Fibonacci sequence: The ratios of successive numbers in the Fibonacci sequence converge to the golden ratio. So, like fractals, the golden ratio unites different areas of mathematics together. Interestingly, it is also found in many places in nature. For example, evidence of the golden ratio has been detected at the quantum level, where magnetic atoms linked together seem to vibrate at frequencies described by φ. On the macroscopic scale, the Fibonacci sequence and golden ratio describe the natural arrangements of seeds and leaves on many plants. If you examine the packing of seeds on the head of a sunflower, there are a series of clockwise and counterclockwise spirals, which generally appear in successive Fibonacci numbers. The plants are precise enough with their math that one especially robust sunflower reportedly had exactly 233 spirals of seeds one way and 144 the other. In addition, the golden ratio can be converted into an angular version (approximately 137.5 degrees), which specifies the rotational gap between successive.
What’s So Special About The Five-Paragraph Essay? Recently, a student asked me what made the five-paragraph essay so important—so special. In short, the student was asking why five paragraphs? Why not three or four or six or seven? Why five? I explained that in my opinion, the five-paragraph essay is more of an instructional technique than it is a piece of writing.  I explained that five paragraphs is a nice number of paragraphs for beginning writers and emerging writers to work with. I explained that many natural patterns of logical thought can be fully demonstrated using five paragraphs. I also explained that many teachers prefer to assign many short essays instead of just a few very long essays, and that students can demonstrate both writing skill and understanding of subject matter in five paragraphs. Put simply, I explained that people just like five paragraphs. There is nothing special about five paragraphs other than that people like working with five paragraphs. I realized after the fact that this last part was not true. There is something special about five paragraphs, just like there is something special about the Parthenon and the art work of Leonardo da Vinci. This specialness has to do with proportion and the Golden Ratio. The Golden Ration is.618, or 61.8% and put simply, the body (the main content) of the five-paragraph essay is very likely 61.8% of the whole essay. This means that the introduction and conclusion (the helping parts) will likely equal 38.2% of the whole essay. If you teach elementary school writing or struggling middle school writers, be sure to check out Pattern Based Writing: Quick & Easy Essay on the homepage. Believe it or not, I needed to examine just four pieces of published five-paragraph writing to find one where the word count of the paragraphs matched this ratio to near perfection. We will take a closer look at this Golden.