The Golden Ratio The Golden Rectangle and Ratio The Golden Rectangle and Golden Ratio have always existed in the physical universe. Nobody knows exactly when it was first discovered and applied to mankind. Many mathematicians assume that the Golden Rectangle has been discovered and rediscovered multiple times throughout history. This would explain why it is called many different names such as the Golden Mean, divine proportion, or the Golden Section. The first person who is believed to have
The golden ratio is a ‘famous’ number that is said to be recurring throughout the world. Architects are said to build with it, painters are said to use it, even sculpter are said to sculpt with it. The Greeks found this ‘Golden Section’ called phi around 500 BC. Phidias was a Greek sculptor and mathematician who is said to have studied phi. Today, there are many claims of where we can find the golden ratio. Whether or not these claims are accurate is the real question. There is a claim that the
The Open Box Problem An open box is to be made from a sheet of card. Identical squares are cut off the four corners of the card as shown in figure 1. Figure 1: [IMAGE] The card is then folded along the dotted lines to make the box. The main aim of this activity is to determine the size of the square cut out which makes the volume of the box as large as possible for any given rectangular sheet of card. 1. For any sized square sheet of card, investigate the size of the cut out
Passing of the Eclipse by Gertrude Harbart When I read the description of the humanities class for school I was not very happy to learn that it was a requirement. I have taken many business classes and that seems to fit right it with what I do. The thought of trying to learn something about pictures, sculpture, literature, dance, film, theatre, and architecture just did not appeal to me. I had actually signed up for this class one other time but after receiving the book and looking through it
this means that it is not very accurate to just divide the answer by 2 because the half squares were not equal sizes and to just divide by 2 would be very inaccurate. Counting Rectangles The next method I will use should be more accurate than the counting squares method. I will split the curve into 5 rectangles and calculate
Intro to Glue Blocks Typical stairs consist of two basic components a tread, horizontal, and a riser, vertical. However, over time stairs begin to degrade causing slight warping in the trend. This shrinkage of the wood as well as weaken of the fastener between the riser and trend causes the two components to rub together, this creates an unpleasant squeaking sound. To solve these problems, a joint called a “glue block” is used with nails or screws to secure the joint to the underside of the trend
INTRODUCTION In the present day world, many schools and educational institutes burden students with the memorisation of multiple surface area formulas for a particular prism. It is vital to have the understanding of how various surface area formulas make geometry appear a hard stream of mathematics. The aim of this directed investigation is to discuss the topic question “Is it possible to develop a general formula for the surface area of any prism” and furthermore to develop a formula that can be
Drain Pipes Shape Investigation Introduction A builder has a sheet of plastic measuring 2m by 50cm, which he uses to make drains. The semi-circle is the best shape for a drain. Prove this. I will prove this by comparing its volume to that of other shapes. On older houses there are semi-circular drains but on newer houses there is fancier ones like pentagon shapes. Is this because they are better or is it simply for design? To find the volume of a 3D object I have to find the
plays themselves. Traditional Greek dress was never shaped for fitted, but draped over the body and was fairly the same for both men and women. All material came straight from the loom and if it was even sewn, it would be a straight seam and a rectangle shape. There are about four different garments that were used in the dress, all very basic and changed through the years. They are: Doric Chiton, Ionic Chiton, Himation and the chlamys. The Doric Chiton was a wool fabric, usually patterned, worn
certain shapes such as octagon and more complex polygons. In such cases, given shapes are split into shapes that have known formulae for areas and the worked out the areas are added together. Areas of the following shapes were investigated: square, rectangle, kite, parallelogram, equilateral triangle, scalene triangle, isosceles triangle, right-angled triangle, rhombus, pentagon, hexagon, heptagon and octagon. Results The results of the analysis are shown in Table 1 and Fig 1. Table 1 showing
Math Fencing Project I have to find the maximum area for a given perimeter (1000m) in this project. I am going to start examining the rectangle because it is by far the easiest shape to work with and is used lots in places (most things use rectangles for design- basic cube .etc). To start with what type of rectangle gives the best result. A regular square or an irregular oblong? I start by having 4 individual squares. [IMAGE] [IMAGE] [IMAGE] [IMAGE] [IMAGE][IMAGE]
The Open Box Investigation The aim of this investigation is to find the largest volume within for an open box with any size square cut out I will be increasing the square cut out by 1cm until I reach a point where the volume decreases. At this point I will decrease the square cut out by 0.1cm until I reach the maximum volume. This will be done on several different grids until I see a pattern which I will then use to create a formula. I will record my results in a table for the different
Investigating How to Get the Maximum Volume From a Cuboid Introduction I am doing an investigation into how get the maximum volume from a cuboid using a square with smaller squares cut out from each corner to then fold it up into a cuboid. Cut out the red squares and fold inwards on the blue lines to get a cuboid. To get the maximum volume from the cuboid you need to work out the sizes of the squares you want to cut out from each corner. The formula I used to work out the volume
Comparing El Grecos St Francis Venerating the Crucifix to El Grecos St John the Baptist The compared works of art, St. Francis Venerating the Crucifix and St. John the Baptist, were both written by the same artist. The actual name of this artist is Dominikos Theotokopoulos, but some people prefer to call him El Greco, which in translation simply means “The Greek.” Both paintings were written by El Greco towards the end of his life, and both are of important religious figures in Christian religion-one
us, it is even in places that you would not think possible or is used in ways that you would not think necessary or practical. The golden ratio,1:1.61, is a ratio that is used to build, design, structure, and even decorate houses. Most houses that follow the golden ratio, 1:1.61, to the exact all look almost the exact same, even though they may vary slightly. The golden ratio appears in everything in nature, from the shape and structure of clouds, the shape and structure of our universe that we live
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
The Golden Ratio Certain pictures, objects, and animals appeal to the human mind more than others. Proportions and images of symmetry often contribute to our fascination with them. Often, when examined carefully, you may find a common “coincidence” between man made objects and those found naturally in nature. This fluke, however, may be used to ascertain various mathematical relationships between these objects. This paper will introduce the golden ratio and weigh its significance on math
Carpe Diem: The Golden Chance Carpe Diem, is the expression that means seize the day, means that one should take advantage of every minute of this life. Many people do not succeed because they are scared about life. It is very difficult to accomplish anything in this life if they do not risk themselves or do not do anything to get what they want. One should enjoy this life in a responsible way. My particular carpe diem philosophy is do the right thing at the right moment. My parents have taught
surpassed the beauty of my childhood paradise, a place my family called Tamarack. Tamarack was a family camp and hunting lodge set deep in the heart of the Mountains. My earliest memories of it are fractured images of sights and sounds and smells--golden bars of sunlight through majestic oaks and elms, the ever-present smell of wood smoke and haunting echoes. I suspect that the setting was the reason for the eerie echoes which resounded about the site. The house, itself, was built on the side of a
Approximately forty-five miles east of Sacramento, California, is the friendly town of Placerville, which marks a major “Gold Rush” historical landmark in the United States. In the early days of this small gold mining boomtown, Placerville was known as “Hangtown.” If you come into town, you will see the sign of Placerville, and underneath it you will see its nickname reading, “Old Hangtown.” Nooses can be seen all over town, on police cars, on historical landmark signs – even at the firehouse and