Shapes and Their Areas
The objective of this coursework is to find out which shapes have the
biggest area. The perimeter must be 1000m, and the shapes can be
regular or irregular.
First of all I will experiment with different rectangles, the
different triangles, then pentagons. Then I will experiment with more
regular shapes (or whatever type of shape has the largest area) to see
the effect on area changing the number of sides has. I predict that
the largest shape will be a regular circle, and the more sides a shape
has and the more regular it is, the larger its area. (Taking a circle
as having infinite straight sides, not one side).
After I have experimented I will try to prove everything using
algebra. I will try and develop a formula to work out the area of any
polygon.
Rectangles
When I looked at the spreadsheet of rectangle areas I could instantly
see that the more regular the shape the larger the area.
However I also noticed that if you turned the graph of for this
spreadsheet upside down you would have a y=xsquared graph, with the
250x250 value being where the y- axis would be.
This means that the area of the values on either side of the square
have a square difference from the area of the square. This is because
if you "move" some of the perimeter (d) from length to with, (i.e.
decrease one dimension and increase the other) the perimeter has not
changed, but the equation for working out the area has.
It changes from
(250)(250) =250 squared
to
(250-d)(250+d) =250 squared - d squared.
So the area difference between a rectangle and a square of the same
perimeter is the difference from one of the squares sides and one of
the rectangles sides, squared.
Because all "real" square numbers are positive, the square will always
have the larger area.
It is very likely that this rule is the same for any shape but I must
[IMAGE] ½ (a2 + b2) times it by the ratio of its real area to a
This shows that there is a difference of 2cm between A and B, and B
"A shape is that which limits a solid; in a word, a shape is the limit of a solid."
Each shape generalizes the personalities and connections of the characters, although not in depth. Atticus is shown to have a big influence on the entire community, always maintaining his maturity and dignity. Scout’s respect is shown, as well as her special understanding connection with Boo Radley. Jem’s big heart and development of maturity can be seen in his shape and the colors designated for each part. Dill’s confident appearance and true insecurity is expressed through the edges of the shape. Calpurnia is shown as a mature caretaker that leads through example, and Bob Ewell is shown as the opposite of every moral the novel is meant to express. When the shapes are put together to create a picture with meaning, the outcome would show the different types of people, not as individuals in Maycomb, but as the actual town of Maycomb, showing that, no matter how old or how young, each person in Maycomb matters.
of view. I actually tried to break that rule later; if you make a rule then you also should
Through Descartes’s Meditations on the First Philosophy, he runs into many dilemmas while trying to rebuild what he knows. One of the most well-known and problematic issue for Descartes is the Cartesian Circle. Even though Descartes believes he solves his problem, many to this day still don’t believe he came to the conclusion he believed he did. Overall, I do not think Descartes properly rescued this problem due to in accurate definitions and lack of distinction and details.
The streetlamp outside paints shapes across the wall next to my bed. I can see them in the darkness, dull orange lines that have become familiar in my many restless nights. At the heart of their canvas, they intersect to form a rectangle. A rectangle? For months I believed in this reality of form with the inborn certainty that accompanies that which is obvious. I didn’t have to think about it. Nightly, I would study the shape in a sleep haze, unconsciously harboring knowledge of its regularity. Except that it is not a rectangle.
* Surface Area - This will not affect any of my results, as we are
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 the areas for the different shapes formed by using the
Using a square, both the length & the width are equal. I am using a
Shapes are two- dimensional surfaces such as circles or squares, and forms are three-dimensional shapes like spheres or cubes. A concave form has a pushed-in surface like the inside of a bowl and a convex form has a raised surface like the outside of a bowl. When you are looking at shapes and forms, the shape that you see first is called a figure or positive shape and the area around it is called the ground or the negative shape. The natural curves in different objects, such as trees or clouds are called organic shapes. Geometric shapes and forms are precise and regular such as cubes, pyramids, and circles. A free-form is an irregular invented shape or form that has qualities of a geometric form or an organic form.
- Suface Area: if you are to change the surface area it is going to
Then in Euclid II, 7, it goes farther to explain that “if a straight line be cut at random, the square on the whole and that on one of the segments both together, are equal to twice the rectangle contained by the whole and said segm...
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.