Shapes Investigation
I am doing an investigation to look at shapes made up of other shapes
(starting with triangles, then going on squares and hexagons. I will
try to find the relationship between the perimeter (in cm), dots
enclosed and the amount of shapes (i.e. triangles etc.) used to make a
shape.
From this, I will try to find a formula linking P (perimeter), D (dots
enclosed) and T (number of triangles used to make a shape). Later on
in this investigation T will be substituted for Q (squares) and H
(hexagons) used to make a shape. Other letters used in my formulas and
equations are X (T, Q or H), and Y (the number of sides a shape has).
I have decided not to use S for squares, as it is possible it could be
mistaken for 5, when put into a formula. After this, I will try to
find a formula that links the number of shapes, P and D that will work
with any tessellating shape - my 'universal' formula. I anticipate
that for this to work I will have to include that number of sides of
the shapes I use in my formula.
Method
I will first draw out all possible shapes using, for example, 16
triangles, avoiding drawing those shapes with the same properties of
T, P and D, as this is pointless (i.e. those arranged in the same way
but say, on their side. I will attach these drawings to the front of
each section. From this, I will make a list of all possible
combinations of P, D and T (or later Q and H). Then I will continue
making tables of different numbers of that shape, make a graph
containing all the tables and then try to devise a working formula.
As I progress, I will note down any obvious or less obvious things
that I see, and any working formulas found will go on my 'Formulas'
page. To save time, perimeter, dots enclosed, triangles etc. are
written as their formulaic counterparts.
This shows that there is a difference of 2cm between A and B, and B
7. "Law of the Twelve Tables." Britannica School High. Britannica Digital Learning, n.d. Web. 3 May 2014. .
In the anonymous poem Sir Gawain and the Green Knight, the character of Sir Gawain is portrayed as the imperfect hero. His flaws create interest and intrigue. Such qualities of imperfection cannot be found in the symbol of the pentangle, which he displays on his shield. This contrast between character and symbol is exposed a number of times throughout the poem allowing human qualities to emerge from Gawain’s knightly portrayal. The expectations the pentangle presents proves too much for Gawain as he falls victim to black magic, strays from God, is seduced by an adulterous woman, and ultimately breaks the chivalric code by lying to the Green Knight.
x 3, 4 x 4 x 4, 5 x 5 x 5, 6 x 6 x 6, 7 x 7 x 7, 8 x 8 x 8, 9 x 9 x 9)
Among the many aspects I noticed, I will focus on your manifestation of this phrase, “A parallelogram whose top and bottom sides are two and a half times as long as its left and right sides”, as stick figures. In this, you had to choose how “a half” would be rendered, and you
In both pieces the Kouros and the Isamu Noguchi Kouros they don’t necessarily have lines as such a painting they both have a form. Both Kouros have linear characteristics that flow through the sculptures, they make your eyes follow the ways of the creases. In the Kouros sculpture from 600 BCE is human like, so it has the way the body is elongated and has those natural lines that make it look human like. The Isamu Noguchi Kouros has negative spaces throughout the piece. All of it is open and it provides a focal area to how the pieces fit within the sculpture. The sculptures both have textures even though they are pictures, just by using my eyes and background knowledge I can tell there is surface that differs in each piece. The Kouros from 600
Race is a matter that has been shaped over many years and through a variety of experiences. We can see through the basis of the Panopticon that we’ve read about in Michael Foucault's, Discipline and Punish, that there is a so called donut shape structure. From both Beverly Daniel Tatum’s, “Why Are All the Black Kids Sitting Together in the Cafeteria?” and Peggy McIntosh’s, White Privilege: Unpacking the Invisible Knapsack, we can tell that the donut shape is due to mostly segregation between races.
A cube a total of 6 sides, when it is places on a surface only 5 of
In conclusion I would like to say that this discussion was not designed to be a proof of why combinations exist but an explanation of how these patterns occur. As you think about how combinatorics show up in Pascal’s Triangle, keep in mind that this is just one of the many patterns that are concealed within this infinitely long mathematical triangle.
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
- Suface Area: if you are to change the surface area it is going to
By using combinations from the above – But this approach has to be made with caution, because confusion can appear in the message.
Fractal Geometry The world of mathematics usually tends to be thought of as abstract. Complex and imaginary numbers, real numbers, logarithms, functions, some tangible and others imperceivable. But these abstract numbers, simply symbols that conjure an image, a quantity, in our mind, and complex equations, take on a new meaning with fractals - a concrete one. Fractals go from being very simple equations on a piece of paper to colorful, extraordinary images, and most of all, offer an explanation to things. The importance of fractal geometry is that it provides an answer, a comprehension, to nature, the world, and the universe.
The ratio for length to width of rectangles is 1.61803398874989484820. The numeric value is called “phi”.