Investigating the Relationship of the Dots Inside a Shape of Different Sizes
AIM: I have been set a task for my coursework to find out the
relationship of the dots inside a shape of different sizes.
PLAN:I have planned to use a specific quadrilateral shape for my
investigation in which lines will be 45o (diagonal), one dot to the
other; touching each others ends and being closed from all sides. I
will be using the following technique for my investigation. First of
all I will commence with the shape-size being 1 cm2 increasing it
every step by another 1 cm2. At the same time I will be counting the
dots inside that particular shape. I will be using this method until I
find a pattern; thereafter I will generate a suitable formula from
that pattern.
METHOD: I will be using more or less 5 diagrams and possibly the 6th
one for my prediction.
[IMAGE]DIAGRAM 1
AREA
DOTS
PERIMETER
1 cm2
1
4
[IMAGE]
DIAGRAM 2
[IMAGE]
AREA
DOTS
PERIMETER
2 cm2
5
8
DIAGRAM 3
[IMAGE]
AREA
DOTS
PERIMETER
3 cm2
13
12
It seems that a pattern is forming for both. Firstly for the dots and
area you add 4, there after you double the number, secondly for the
perimeter you just add four at each level.
DIAGRAM 4
[IMAGE]
AREA
DOTS
PERIMETER
4 cm2
25
16
DIAGRAM 5
[IMAGE]
AREA
DOTS
PERIMETER
5 cm2
41
20
I have realised that the comment I made before for the dots and area
is incorrect. What I said was that after starting with four the number
will double itself on each stage i.e. 4, 8, 16… etc.
PREDICTION: I think that the shape with the area of 6 cm2 will have 61
as we will be following the same set of steps each time we collect a
First, we had to measure each of the lines (Lines A-J) in inches and centimeters.
22 CH2 units long, but it is always an even number because of the way
After the calculation we needed to convert pc to meters so we used the calculation factor of 1pc=3*10^16m
3. Place the end of the ruler at one edge of the crater and measure to
thickness 34 mm and length 30 cm at the same point on the ends of the
that for this to work I will have to include that number of sides of
If I had the chance to complete this task again, I would have executed it in a different approach. Instead of a square/rectangle base, I would have gone with a triangular base.
triangle has a side of 4 and it looks shorter than the side of 3. The
The purpose of this experiment was to determine the effects of voltage and molarity changes on the fractal dimension of a Cu crystal formed by the re-dox reaction between Cu and CuSO4. Using the introductory information obtained from research, the fractal geometry of the Cu crystals was determined for each set of parameters. Through the analysis of data, it was determined that the fractal dimension is directly related to the voltage. The data also shows that the molarity is inversely related to the fractal dimension, but through research this was determined to be an error.
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.
Surface area of right cylinder (SA) = 2 π r2 + 2 π r h square units
... your destination gets closer (divided in half) the time interval to get to said destination gets shorter. Ever decresing periods of time can be thought of as the same as with the Achilles paradox. Once again we can pull the converging infinite series and make a finite point in which the journey begins. Once we begin the journey the rest is cake.
The Golden Rectangle is a unique and important shape in mathematics. The Golden Rectangle appears in nature, music, and is often used in art and architecture. Some thing special about the golden rectangle is that the length to the width equals approximately 1.618……