This applet deals with problem #19 on page 10. As you can see, I have a trapezoid and a parallelogram. The important part of this problem is the diagonals within both shapes. As you can see, the trapezoid has adjacent congruent half-diagonals, I guess you would call them, while the congruent segments in the parallelogram are on opposite sides. Thus the parallelogram diagonals bisect, while the trapezoid ones do not.

Now for a bit of explanation on this puppy. As you will see, I is the midpoint of AC, and J of DB. Now... oh wait? What is this? The midpoint of I and J, K, also happens to be the intersection point of the internal parallelogram's bisectors?!? I wonder why this could be... If you want more explanation on this phenomenon, google Varignon's Theorem. Essentially, this applet proves that theorem.

Some belated applets:
Finally got these to upload. Sorry for the wait.

This may be the coolest applet ever. Please note that I didn't make this myself; I simply slimmed it down so it would fit better and be more appropriate for the wiki. The original applet can be seen at here. It was designed by Chris Sangwin and is titled "The Harmonograph."

For those of you who don't know what a harmonograph is, it is a contraption, originally a Victorian parlor toy, that creates an image of a musical note. The Duke Energy Children's Museum has two harmonographs, so I'm pretty knowledgable about their history and relation to musical theory. This applet, however, has all the math behind the cool images. Enjoy!

Here's the challenges from the last two weeks. I'll add text soon:

Various Centers of a Triangle
Also pretty boring...

Perpendicular intersecting Lines
A bit boring, I know.

The Cannon Game
I designed the whole thing, though the idea was inspired by Raphael.

Here is a fun thing i made during study hall. Simply choose positions for the two big Xs (reflections across the x or y axis generate the best results) and drag the big black dot around. Tada! Pretty Rainbow.

Thanks to Evan for realizing that the colors can be moved around. Try adjusting where the colored circles start!

Also I added tabs for turning off specific colors.

Leave all comments or suggestions in this pretty box please!

This applet deals with problem #19 on page 10. As you can see, I have a trapezoid and a parallelogram. The important part of this problem is the diagonals within both shapes. As you can see, the trapezoid has adjacent congruent half-diagonals, I guess you would call them, while the congruent segments in the parallelogram are on opposite sides. Thus the parallelogram diagonals bisect, while the trapezoid ones do not.

Now for a bit of explanation on this puppy. As you will see, I is the midpoint of AC, and J of DB. Now... oh wait? What is this? The midpoint of I and J, K, also happens to be the intersection point of the internal parallelogram's bisectors?!? I wonder why this could be... If you want more explanation on this phenomenon, google Varignon's Theorem. Essentially, this applet proves that theorem.

Some belated applets:

Finally got these to upload. Sorry for the wait.

This may be the coolest applet ever. Please note that I didn't make this myself; I simply slimmed it down so it would fit better and be more appropriate for the wiki. The original applet can be seen at here. It was designed by Chris Sangwin and is titled "The Harmonograph."

For those of you who don't know what a harmonograph is, it is a contraption, originally a Victorian parlor toy, that creates an image of a musical note. The Duke Energy Children's Museum has two harmonographs, so I'm pretty knowledgable about their history and relation to musical theory. This applet, however, has all the math behind the cool images. Enjoy!

Here's the challenges from the last two weeks. I'll add text soon:

Various Centers of a TriangleAlso pretty boring...

Perpendicular intersecting LinesA bit boring, I know.

The Cannon GameI designed the whole thing, though the idea was inspired by Raphael.

Here is a fun thing i made during study hall. Simply choose positions for the two big Xs (reflections across the x or y axis generate the best results) and drag the big black dot around. Tada! Pretty Rainbow.

Thanks to Evan for realizing that the colors can be moved around. Try adjusting where the colored circles start!

Also I added tabs for turning off specific colors.

Leave all comments or suggestions in this pretty box please!

A theme song for our class, I think. Mr. Phelps's pen casts auto tuned.