### What is a Transformation?-

A transformation is a term for specific ways to change a shape from its location, size, or direction. The original image is called the pre-image and the new one is called the image.

#### What are the TRANSFORMATIONS?-

- Translations
- Rotations
- Refelctions
- Dilations

Now, let's discover these transformations and other interesting mathematical phenomena in real life!

#### 1. TRANSLATION

In this portion of our presentation, we are going to discover translations. First of all, what is a translation?

A translation is one of the transformations. It changes the location of the pre-image. Here's an example on paper:

A great example of using translations in real life is a level. The tool in the background is called a level. The level is a tool that tests if a surface is level or not, the bubble inside the glass tubes are very sensitive, if the surface that it's on is not even, the bubble will slide (translate).

Let's take a look at some other examples...

A floor washer is another good example of using translations in real life. It slides (translates) across the school floor to clean it. A similar situation happens with a zamboni and a floor waxer.

A slide is also based on using translation, people sit on the slide and they slide down (translate). This is quite interesting because I this example people translate for fun!

#### 2. ROTATIONS-

The next transformation we will discover is the *Rotation.*

A rotation changes the location and/or direction of the pre-image. A rotation happens when a something turns around a certain point.

A swivel chair is a great example of how rotations can make lives easier. The swivel chair *rotates *around the base rod of the chair which is the point of rotation. This allows the person sitting in the chair to move 360 degrees around. This is optimal movement and can allow for quicker movements in the office cubicle or workspace. That means that when you're working on that big project and need to grab a notepad, pencil, or stapler you can just swerve around to grab them.

Here are some other examples...

Yep, there's a company who sells spinning tops as a business!

Yep, those small spinning toys we used to make is a great example of* orbit rotation.* Orbit rotation is when an object is rotating around a point of rotation, while also rotating itself! It's very similar to the orbit of planets, hence the name orbit rotation. Spinners like these made life more fun in the younger years.

Rotation can also be used for entertainment or beauty, proved by the ferris wheel.

#### 3. Reflections (and symmetry)

Now, let's discover reflections and symmetry!

A reflection is a transformation that changes the direction and/or location of the pre-image.

That means that if a reflection happens, then the direction and/or location should change depending on the where the reflection line is residing.

Water Beauty

Water is possibly the most beautiful example of how transformations can elegantly show up around us through nature (or man-made products). The image seen right now is breath-taking, and also a great example of reflections through water. The shore and horizon could be the reflection line, while the mountains and sky themselves would be the pre-image! There were other even more beautiful photos, but none of them had the perfect clarity of the reflection like this one...

Let's discover some other scenarios...

Another beautiful example of nature naturally reflecting is leafs! No, not the team that hasn't been good for 24 years, leaves that grow on trees! Leaves even have a gorgeous tendency to include a reflection line is as seen through this leaf.

This small bucket thingy is a simple but effective example of reflections appearing in the world that we don't even recognize!

#### SYmmetry

Symmetry is two exact same parts facing off one another. IN FACT, symmetry IS an example of reflections.

Ah yes, the classic example of symmetry. A snowflake shows the utter perfection nature can create that involves transformations (aka MATH)!

This Boeing 747 airplane shows how symmetry is useful in real life! Without this symmetry, aviation would not work. Aviation requires balance & motion, which means the shape must be symmetrical.

#### 4. Dilations

Finally, we will discover dilations! So, what is a dilation?

A dilation is a transformation that changes the size of the pre-image.

That means that when the size of something changes while the shape and ratio are still maintained, it is known as a dilation. When you hear the word dilation, you might think of an eye dilating, which is correct. Since the eye's shape remains the same while growing or shrinking it's a dilation.

An example of dilations would be models o anything such as helicopters. Models of objects are a great example of how dilations are useful in real life. You can test the aerodynamics, balance et cetera, without needing to use or waste the actual object.

This photo here is just to prove that this indeed, is a dilation and not a* similar shape,* which we will discover later.

Let's check out some of the others...

These two cans of Coca Cola™ is a cute example of dilations appearing without us even noticing!

#### Similar Shapes

A similar shape is 2 shapes that have mainly the same shape (duh...) and dimension ratio, just a different size. It's pretty much a dilation in disguise.

This is an adorable example. It can also be taken as an example for a dilation, though it cannot be the EXACT same shape.

### The Beauty of Transformations

Look, sometimes we can forget that Math can be found and used in real life! These are just some examples of what happens when you seek to discover math in real life. If you still don't truly believe us, take a look yourselves!

(The first 10 photos in the photo grid above are original, while the others aren't).

Thank You for Watching a Dvij Barot & Josh Wu Production

(SPONSORED BY COCA COLA™)

Credits:

Created with images by fdecomite - "A Stella Octangula inside a Rhombic Dodecahedron" • www.metaphoricalplatypus.com - "Waterslides" • woolennium - "ferris wheel - irvine spectrum" • skeeze - "sunrise landscape scenic" • tsuna72 - "Touched Up" • skeeze - "sunrise landscape scenic" • woolennium - "ferris wheel - irvine spectrum" • www.metaphoricalplatypus.com - "Waterslides" • tsuna72 - "Touched Up"