Ellipses

Picture of how Circles and Ellipses are formed

I was fascinated when I learned this in Geometry.

Everyone knows what a circle is- it is a series of points that are the same distance from a center point. Now, what is an ellipse? The definition is a little more complicated: a closed plane curve resulting from the intersection of a circular cone and a plane cutting completely through it; the sums of the distances from the foci to any point on an ellipse is constant.

Drawing an Ellipse

The picture on the right demonstrates the first part of the definition. Here's an example of what the second part means: Suppose you want to draw an ellipse. You take two tacks, push them into a piece of paper, and you tie each end of a string that is longer than the distance between the two points to the tacks (each end of the string is tied to a thumbtack). Finally, you push a pencil against the string so the latter is tight (see picture on left). Now if you move the pencil around the tacks, keeping the string tight, you will end with an ellipse. It is a very neat method of drawing an ellipse, but what does this have to do with "the sums of the distance from the foci to any point on an ellipse is constant"? Well, unlike a circle, an ellipse has two foci (plural for focus). If you draw an ellipse using the method stated above, the place where you had your tacks will always be the foci. Now notice how the lines in the picture have names- F1 and F2. In the end, then, statement "the sums of the distance from the foci to any point on an ellipse is constant" simply means that F1 + F2 will always be the same number.

Roller Coasters, Part 1

Traditional Chain-Lift Method

Roller coasters definitely deserve to be on the list of epic inventions. They're huge pieces of art that date back to the early 1800s. Roller coasters satisfied man's need for speed, and they quickly became bigger, better, and faster. In this post, I will list some lift methods of roller coasters...

The first and traditional method is the lift method. This can mean either of two things: (a) a long loop chain that is powered by motors and moves in the uphill direction continuously. Hooking onto the train when it arrives (you're most likely to see this method), and (b) a series of tires that rotate in the same direction up the hill (this is more commonly found on small coasters).

The second method is the launch method. This is a great method because riders don't have to wait while they're slowly pulled to the top. A few types of launch roller coaster are (and a very brief description):

• Electromagnetic (uses electricity to set off magnets that, in turn, pull the car across the track until it has enough momentum to get up the hill)
• Hydraulic (uses compressed hydraulic fluid to turn a turbine which spins and pulls a cord attached to the train)
• Pneumatic (similar to the hydraulic except using compressed air instead of fluid)
• Electric motor with spring tension (motor pushes spring until it is tense, then releases the train)

A few other types of lifts are...

• Elevator lift (what the name implies; a piece of track detaches and moves vertically to connect with the other end of track at a higher altitude. For example, the Matterhorn Blitz at Europa-Park).
• Ferris Wheel lift (it is amazing. You must watch a video to understand it. An example is Round About at Freestyle Music Park).

Solving a Rubik's Cube

Who hasn't heard of a "Rubik's Cube"? Whether it is unsolved and hidden away, or solved and proudly displayed, almost everyone in the world owns one. It is 3-D puzzle that has a very simple concept, yet has over 43 quintillion possible configurations, it seems that it would be very hard to solve. However, a large number of people have solved it. How? Well, here are some solutions...

1. Take off all the stickers and replace them in the correct way (I'm pretty sure this is classified as cheating ;)).
2. Memorize a bunch of algorithms (this is how I did it).
3. Build a robot that does it for you (this is my personal favorite, although it would be way harder than simply memorizing the algorithms). Below is a video a robot solving a Rubik's cube. The robot was created by Mike Dobson, and was made with LEGO Mindstorm elements. LEGO Mindstorms is an awesome set, and I own one myself. You'll probably see more posts including Mindstorms in the future. For now, enjoy the video. :)

Yeah, that video was awesome. In fact, it was the main reason why I wanted to make a post about Rubik's Cubes. Another reason is because they're fun to solve, easy to take with you wherever you go, and they also make a great gift!

Do you want to learn how to solve a Rubik's Cube? Here* is a great website that'll get you going! If you have any questions, please ask!

*the website is not owned by me. Use at your own caution ;)