Math Borders Investigation
Figure below shows a dark cross-shape that has been surrounded by
white squares to create a bigger cross-shape;
The bigger cross-shape consists of 25 small squares in total.
-------------------------------------------------------------
The next cross-shape is always made by surrounding the previous
cross-shape with small squares.
Part 1- Investigate to see how many squares would be needed to make
any cross-shape built in this way.
Part 2- Extend your investigation to 3 dimensions.
[IMAGE]
Introduction -
I am doing an investigation to see how many squares would be needed to
make any cross-shape built up in this way. Each cross-shape is made by
using the previous cross-shape and adding another layer of white
squares, making all the inner squares black. The first cross-shape in
the sequence is a single black square.
To start my investigation I must draw the first 7 cross-shapes. This
will enable me to see a pattern in the shapes so I can make a table
and record how many black and white squares there are in each
cross-shape I have drawn. From my table I must use the results to work
out formulae for black, white and total number of squares.
After this I will test the formulae on a pattern I have already drawn
and on one I have not already drawn.
I will be working systematically in my investigation because if I work
in a
particular order it will be easier for to see a pattern and links in
the sequences.
Finally I will be looking at different ways of getting the formulae
and also extending my investigation into 3 dimensions.
Part 1
Drawing the cross-shapes
Pattern 1 Pattern 2 Pattern 3 Pattern 4
---------------------------------------
[IMAGE]
[IMAGE]
[IMAGE]
[IMAGE]
Pattern 5 Pattern 6 Pattern 7
-----------------------------
[IMAGE]
[IMAGE]
[IMAGE]
Here is my table of results telling me how many black, white and total
numbers of squares there are in patterns 1 up to 7.
6x6x6 cube and see if I can find a pattern. When I have found a
Shapes are the first symbols that can be seen throughout the story. For example, the black box, and the town square are square shape. A square represents Shirley states, “the people of the village began to gather in the square.” Circles are also shown in the stool and in the white paper. Shirley Jackson wrote, “it had a black spot on it.”
What will you do when you meet a wall that block your way? There are only two ways, either finding a way to go through the wall or staying still. In fact, this is life, when a barrier cut down the road, there comes to two choices, taking an action or doing nothing. In poems ‘where there’s a wall’ by Joy Kogawa and ‘Paxis’ by Sharon. They both talk about the ‘walls’ in their life. On the one hand, in ‘where there’s a wall’ Joy tells about her experience inside the internment camp where there is no freedom. On the other hand, Sharon in ‘Paxis’ observes how human being act meaninglessly under control of outside world. He expresses his sorry and wants to encourage people to fight their own future. Joy and Sharon try to tell people, life can be full
a level area of land. She is not concerned about the shape of the plot
cube, I noticed that all of them had three faces. I then went onto a
Principal 2: A suveyor creates land boundary lines. These created lines, which are separate and distinct from property lines, are determined by legal principals and law.
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
The Thin Blue Line is a symbol of honor to most and corruption to some, but the mainstream media has portrayed it as a symbol of maleficence and betrayal to the people. This symbol isn’t just for those Police Officers that wear the badge over their heart day in and day out. It’s for the 99% of citizens who live an unsullied lifestyle as well. I am extremely proud to be within the ranks of the aforementioned group. The Blue represents the Police Officer and the courage they find deep inside when faced with the insurmountable odds of violence. The first half of the black is a reminder of our fallen brothers and sisters. The second half of the black is the law abiding citizens that support law and order. If rogue behavior or maleficence
I am going to begin by investigating a square with a side length of 10
A Positive Outlook on Math Manipulatives Math manipulatives have been around for years, but are now becoming increasingly popular amongst educators. Math manipulatives include anything from buckets of pattern blocks, trays of tiles, and colored cubes to virtual manipulatives, or manipulatives colored and cut out by the students themselves. All of these materials can help assist in teaching children math concepts by pulling math off the page and into the hands of students. For a child to be verbally and physically taught, a math concept allows them to think, reason, and solve problems with the teacher's guidance as well as on their own.
P²+11P+10 -P² - 11P = 10 As it shows the result is 10 once again
3. The pattern diagram is very essential in creating a crochet product. This serves as the guide on how he will follow the instructions and outline of the design. Most patterns are usually easy to follow especially if the person is highly skilled n crocheting. For most beginners, there are patterns, which are more basic and simple. They are especially designed for them to practice and understand simple patterns of crochet products.
In this paper, I will explain three theories on how to solve the demarcation problem, or the problem of distinguishing between science and non-science, and how all three of them need to be combined in order to truly solve this problem. First, I will explain each of the three different theories proposed by A.J. Ayer, Karl Popper, and Paul Thagard, these philosopher’s arguments for each of these theories, and an example of using each theory. Then, I will explain why all three of these theories need to be combined by showing examples of how each individual theory incorrectly categorizes something as scientific. Next, I will show how these three theories together can correctly distinguish science from non-science. Finally, I will explain various refutations to this argument and defend against them. Demarcation is important, because only science can be proven or disproven by facts of nature. All non-science are just theories created by man – hypotheses that cannot be supported by reality.
Materials : Manilla card of different shapes which have a surface area of 400.00cm² (circle, triangle, square, hexagon, octagon) , stopwatch (±0.01s), metre rule (±0.05m)
The Nature of Mathematics Mathematics relies on both logic and creativity, and it is pursued both for a variety of practical purposes and for its basic interest. The essence of mathematics lies in its beauty and its intellectual challenge. This essay is divided into three sections, which are patterns and relationships, mathematics, science and technology and mathematical inquiry. Firstly, Mathematics is the science of patterns and relationships. As a theoretical order, mathematics explores the possible relationships among abstractions without concern for whether those abstractions have counterparts in the real world.