Tessellation is the process of repeating geometric shapes to form a pattern. These patterns do not contain any gaps, or overlaps of the geometric shape. Tessellation in everyday life can be seen in mosaics, tiling, art, and even in nature. A bee hive or honeycomb is a great example of the natural tessellation. When I first saw the assignment for this week, I assumed it would be easy to do. However, the actual process of making the pattern was harder than expected. The concept seems easy enough; the application is where I struggled. I also found using the paint application harder because the image is not easily formatted to fit on a piece of paper. I had to adjust and readjust the image multiple times in order for it to be seen properly. The type of transformation used in this tessellation is the flip transformation. I used one image and reverse it back and forth to form a pattern. I chose the figure because it was an easy shape to draw and manipulate. I found as I tried to create a pattern the more intricate the figure, the harder it is to form a coherent pattern. By using a simple pattern I was able to manipulate it with flipping to form an interesting and intricate pattern.

In all, this is a great activity for students, but I think I would help simplify the method for younger children by having cutouts of different shapes for them to use. This would enable my students to use uniform shapes to form their tessellation, rather than rely on multiple tools to draw it precisely. I can understand where the younger students would have a harder time understanding and applying the concept of tessellation. As an adult, I found the task difficult to apply on paper. The image and what I wanted to do with that image was clear in my mind, but I needed to form a way to translate that onto the screen. As younger children the use of paint programs and other technologies may not be readily available and to form a tessellation purely by hand is a more...

...Tessellations
2013
Jessie & Sheena
Math 1900 – FINAL PROJECT ESSAY
4/3/2013
Tessellations
Introduction
Tessellation comes from the Latin word “tessella” which is a small stone or piece of glass used to make mosaics. Tessella means small square and is usually referred to as a tile. A tesselation is a 2 dimensional tiled plane with no overlaps or gaps. Tessellations can be found in the form of art, nature and best known for tiling floors. Throughout the essay we will be discussing the mathematics behind tessellations, the creator, Escher and how he manipulated them into works of art as well as Penrose Tilings introduced by Roger Penrose and how he brought a new twist to tessellations.
Math Behind Tessellations
In order to create a regular tessellation the first step is to choose one single regular polygon, whether it be an equilateral triangle, a square, or a hexagon, these three regular polygons are the only prototiles that will tile the field with no overlaps or gaps when completed. The rule for regular polygon is that all sides are the same length and all angles are of the same degree. A regular polygon has rotational and reflexive symmetry. Reflectional symmetry is when a shape can be cut directly in half and be identical on both sides. Rotational symmetry is when an object can be rotated on any degree and remain its original...

...Tessellation | |
| By: Lee Pak Long8B23 |
By: 8B (23) Lee Pak Long
So, what is “Tessellation? According to the dictionary, Tessellation is the process of creating a pattern using the repetition of a shape with no overlaps and no gaps at all, which the word “tessellate” comes from
the Greek word “Tesseres” ,which means “4”.
Otherwise, comprehending in a simpler manner, a way to tile a floor. Also, the puzzle you did last time is also a tessellation actually.
Since primary school, we have learnt about 2D tessellation, which can also be found in our mother nature. When basaltic lava flows they mostly have cracks on them caused by contraction forces, creating columns of harden lava which resembles the tessellation of regular hexagons. One of the most famous example, the Giant’s Causeway in Northern Ireland.
Tessellations can also found in daily life. For example, the tilings on the floor, toilets etc.
For regular tessellation mentioned before, there are actually only 3 types of regular polygons which can be tessellated by themselves, which is :
1. Triangles
2. Squares
3. Hexagons
Only three regular tessellations exist, because there are only three polygons whose interior angles divide evenly into 360 degrees: the triangle (60 degrees) the square (90 degrees) and the hexagon (120 degrees).
Of the regular...

...“Shapes On Me”
Shapes are every where
In every place I stare
Rectangle in the building
Sphere drawn on the side walk
Hexagon on the stop sign
Circle in the number nine
Triangle in the pyramids
Octagon on the jewelry box lid
Stars in the sky
Oval in Ma’am Granada’s eye
Pentagon in Washington dc
Square in my TV
Shapes are every where
In every place I look
Now I can figure out what shapes I see
If only I could find my geometry book
"On Behalf of the Sides of a Triangle"
Oh, triangle, I wish I knew why
You're known for three angles instead of three sides
Your angle's a cute part of you, I agree
But you're being obtuse if your sides you don't see
For what could be more necessarily true
Than that two sides must meet to form angles for you
And it is the length of your sides, after all
That determine if you are gigantic or small
Yes, even the straightness your sides show is key
(If two sides were curved, you'd look more like a D)
So from now on I'll boycott the triangle shape
Remove it from my geometric landscape
And some day I hope the whole world will decide
That instead of triangle, they'll call you triside
“The Geometry”
Horizontal, parallel, intersecting, perpendicular
Different widths, lengths, heights, numbers
Base times itself gives the square's area
In a circle, radius is half the size of the diameter
Calculations, facts, theories to conquer
Angles...

...
What is a tessellation? A tessellation is the creation of a two dimensional plane with the use of a geometric shape repeatedly and leaving no gaps. Tessellations can be found everywhere in our daily life and also in nature. For example of tessellations that can be seen anywhere is the sidewalks that you walk on, even though it’s a simple tessellation it is still atessellation. Another example of a tessellation that can be seen in nature is a beehives comb, the pattern in side is a tessellation made of octagons which stores honey.
The word “tessellation” got its name from the latin word “tessella” which mean small cube. The history is of tessellations are actually very short. In 1619 Johannes Kepler one of the first people to make record of tessellation when he wrote about regular and semiregular tessellation, which are coverings of a plane with regular polygons. In 1891 a Russian crystallographer Yevgraf Fyodorov proved that every periodic tiling of the plane features one of seventeen different groups of isometries.(source taken from Wikipedia)
M.C Escher a famous dutch artist who uses tessellations in all of his art work. M.C Escher is not only just an artist but a math major. In every artwork of Escher is has many...

...
Tessellation Patterns
MTH/157
Tessellation Patterns
Tessellation Patterns are a way to express creativeness. A tessellation is a repeating pattern of shapes covering a plane without any gaps or overlaps. Choosing a pattern with triangles that are black and white was a way to express a pattern. There are so many different ways to create a tessellation pattern and use of transformation. Normally, tessellations are created using polygons, this one was created using triangles.
Reflections occur across a line called the axis. To reflect a shape across an axis is to plot a special corresponding point for every point in the original shape. Specifically, the corresponding point is the point that is the same distance from the axis as is the original point. You determine the distance from a point to a line by drawing a line perpendicular to the original line and that passes through the point.
Working with simple lines of symmetry will make this pattern clean and simple with black and white colored triangles for the pattern. This pattern is a reflection of itself so when that it is folded in half either way the reflection will show on the other side as the same. Working with many patterns and colors to make different designs can be quiet confusing in the way they turn out.
There are so many ways to work with a...

...No. FC2013-053895
)
)
)
)
)
)
)
Respondent )
Natalie Camarillo-Cobb
Petitioner
and
Shawn Laidlaw
Child Support Worksheet
(June 1, 2011 Guidelines)
DOB: 02/13/2013
AGE:
1
Youngest Grade Estimated:
Actual Grade:
Presumptive Termination Date:
May 31, 2031
Children 12 or over: 0
Number of Minor Children: 1
Primary Custodian is: Petitioner
Petitioner
1,100.00
Court Ordered Spousal Maintenance (Paid) / Received
[Mandatory]
Custodian of P: 0 R: 0 Other Child[ren] Subject of Order
3,500.00
[Mandatory]
Court Ordered Child Support of Other Relationships (Paid)
3,500.00
1,100.00
Gross Monthly Income:
Respondent
[Mandatory]
Support of P: 0 R: 0 Other Child[ren] Not Ordered
[Discretionary]
Adjusted Gross Income:
Combined Adjusted Gross Income
4,600.00
Basic Child Support Obligation For 1 Children:
814.00
Additions to Child Support Obligation:
Adjustment For 0 Children Over Age 12 at 10 %
[Discretionary]
Medical and Dental Insurance Paid By
[Mandatory]
Monthly Child Care Costs For 1 Children Paid By
[Discretionary]
800.00
Less: Federal Tax Credit (25%) Allowed To Custodial Parent:
Extra Education Expenses Paid By:
[Discretionary]
Extraordinary (Gifted or Handicapped) Child Expenses Paid By:
[Discretionary]
Total Child Support Obligation
1,614.00
Each Parent's Proportionate Percentage of Combined Income
23.91 %
76.09 %
Each Parent's...

...Shapes
Everything around us is made of shapes, from the smallest type of micro-organisms to the biggest structure you will ever see in your life. They are the faces of the 3D solids we see around us, either being there in its own, or being a mix between two or more polygons. Shapes resemble different things and delivers different thoughts when looking or passing by them through the day. Putting these shapes or joining the to form volumes gives as a huge number of volume, they could be in the form of
Cubes Pyramids
Cylinders Rectangular prisms
Cones Spheres
One of the solid structures that fascinated architects and artists throughout ages is the “Platonic Solids”. Till now many breath-taking huge structures are inspired by these polyhedrons. It is also found in nature in micro-organisms, crystals, molecules and many other forms. Even these solids are made of 2D shapes, especially 3 shapes: the triangle, the square, and pentagon polygons. These 3 simple shapes give those solids a unique symmetry impossible to find in any other polyhedron.
Every shape has a concept behind it that affects the eye and brain when subjected to it, and...