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
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
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
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
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
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
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
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
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
where we can find the golden ratio. Whether or not these claims are accurate is the real question. There is a claim that the golden rectangle whose sides have a 1:1.618 ratio is the most esthetically pleasing. Having tested this theory in class, there is no proof of validity. In our class, out of approximately sixteen students, only one picked the golden rectangle. In the
Geometry is used in everything in the world around 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
We search for rectangles with dimensions such that the expression is represented by 2-digit & 4-digit Jarasandha numbers. In the above expression , & denote the area and semi-perimeter of the rectangle respectively. Also, total number of rectangles, each satisfying the above relation is obtained. Keywords: Rectangles, Jarasandha numbers. 1. Introduction Mathematics is the language of patterns and relationships, and is used to describe anything that can be quantified. Number theory is one
the plan by looking for geometries, regulating lines, and interior/exterior relationships within the massing. I found a grouping of rectangles as the prominent geometry. None of the rectangles are separated from the rest. The interior space is the largest rectangle with the entryway at the bottom that aligns to the diagonal. The exterior space is the smaller rectangles that group around the main interior space. The regulating lines that I uncovered seemed to regulate the geometry and size of the building
Maxwell was the Reverend of the First Church of Raymond. At the beginning of the novel, he viewed the Rectangle, an area in the town of Raymond, and other places like it with fear and dislike. This was because these places were full of sin, drunkenness and immorality. He did not believe that it was a city full of children and disciples of God. An example of Maxwell’s view of the people in the Rectangle is how he responded to the tramp, Jack Manning in the first chapter of the novel. Jack had been
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
A rectangle is a very common shape. There are rectangles everywhere, and some of the dimensions of these rectangles are more impressive to look at then others. The reason for this, is that the rectangles that are pleasing to look at, are in the golden ratio. The Golden Ratio is one of the most mysterious and magnificent numbers/ratios in all of math. The Golden Ratio appears almost everywhere you look, yet not everyone has ever heard about it. The Golden Ratio is a special number that is equal to