A Geometric World

A Geometric World By: Sanya and emmie

Reflections

Just Keep Swimming!

Blub! Blub! Blub! This image of a turtle swimming in the water is a real life example of a geometric transition-a reflection! As you can see, in this image the turtle's picture is reflected in the water. A mirror image of the sea turtle is shown!

The Bean!

The Bean! The image of this work of art also displays the geometric transition known as a reflection. The Bean is reflecting a city scape. It is just like a mirror! Anything that you view in a mirror is a reflection!

This image shows a real life example of a reflection. The buildings in the background are displaying the reflection that is taking place. The other buildings surrounding the mirror-like buildings are being shown/reflected.

Transitions

Kites Ahoy!

The image of these kites displays another type of geometric transition! This transition is known as a translation. As you can see, it is as if these kites were translated or slid across the sky, resulting in the same kite being shown repeatedly!

Bright Lights!

The image of a city from a bird's eye view is another real life example of a translation! As you can see, in this image it appears as if the lights of the city are being translated across the ground. Resulting in many lights being shown!

Don't Let The Sun In...

These images of the curtains drawn and open display a real life application of a translation. The curtains are translated to the right and left to open them and let it in the light!

Rotations

Giants...

Giants..not the monstrous kind, but a trick in gymnastics! In this image the gymnast is preforming a 360 degree rotation around the high bar!

Something's Cooking!

What's cooking? This image of a gas stove top displays a geometric transition, a rotation! The one dial on the stove top is rotated, resulting in the stove turning on! One can see the original position of the remaining three dials as showin in the picture.

Tornado Kick

This is called a tornado kick in Karate. As one can see a full rotation is displayd while performing th kick. This is a real life example of a rotation. Emmie is also being translated while performing the kick!

Similar Shapes, and Dilations

Vroooommmm

This image is a real life example of a dilation, or similar shapes. Dilations and similar shapes are the same! As you can see, the real car and the toy replica of the car are the same shape, they are just not the same size!

The Two Twin Plates

In this image, the two plates are identical in shape! But, they are not the same size. Therefore, this is an example of a dilation as these two shapes can be identified as similar shapes!

Cold-Shoulders...

This image of two cold shoulder sweaters displays an example of a real life application of a dilation! These sweaters are the exact same in shape and design, the are just not the same size!

Any piece of clothing that you view at a store most likely has a dilated similar shape! You can find many sizes in a specific piece of clothing making the collection similar shapes!

Symmetry

Beauty In Nature

A natural beauty! This image of a peacock feather displays yet another geometric wonder! As you can see, the two halves of this feather are symmetrical! Meaning that they are identical.

Green Goodness

In this image there is a kiwi that has been cut in half. The two halves of the kiwi are a mirror image of each other. There can be an invisible line of symmetry draw between the two halves to show that they are symmetrical!

Rose's are Red, Violets are Blue...

This image of this beautiful pink flower displays symmetry in real life! If a line was placed down the middle of this flower, the two halves of the flower would become symmetrical! Obviously this flower could be split in more than one direction

Glossary

Reflection-a reflection is a geometric transformation in which an image is reflected or flipped over a line resulting in a mirror image of the original. The line of reflection can be be can anywhere, and can be identified as when should be able to see where the shape is being flipped.

Translation- translations are another type of geometric transformations. In a translated image the image is slid or translated in any direction (left, right, up, and down). To be able to see what directions an image is being translated one uses a translation vector. In a translation vector there are positive and negative numbers that correspond the order of (x, y). A negative number in the x means that the image is moving to the left, if it's positive it is moving to the right! If the number is negative in the y the image is being translated down, and if the number is positive the image is being slid up!

Rotations-Rotations are one of the three most common transformations. In a rotation an image is rotated or spun around a certain point. This point is mathematically called "the point of rotation".

Similar Shapes/Dilations: similar shapes are shapes that are of the exact same shape but not the same size. Therefore, they are proportional. A dilation is when a shape is made smaller or larger. The amount by which the shape is increased or decreased in size is known as the scale factor. If the scale factor is NOT a whole number, the image is getting smaller. If the scale factor is a whole number the image is getting larger. Once the images are dilated they can be called similar shapes!

Symmetry-a mirror image of a shape is created when it is translated, reflected or rotated. The most common type of symmetry is Reflection Symmetry. This is when a shape is reflected over a line, resulting in a mirror image! Rotational Symmetry is when an image is is rotated around a certain point so that it appears two or more times. The number of times it appears is called the order. Point Symmetry is when each point on an image is the same distance from a central point, but it is going in the opposite direction.

Appreciate

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