Bent Shower Rod

This past week I went to Monterrey with my mom for a little vacation. We stayed in a small hotel and while there I noticed the bent shape of the shower rod. I immediately thought of geometry.

After drawing in a straight bar and calculating the area of the triangle formed versus the increased area with a bent shower rod:

I concluded that the bent rod greatly increases the space within the shower.
37.31-21.63= 15.68 cm-squared more space.

This is probably one of the simplest yet one of the most useful inventions for everyday life. (~LU2)

Cymbals with Tangents, Chords, & Secants

Over the weekend, I acquired two new cymbals and I thought I'd make use of them, other than for music.  In this first illustration, I proved that the result of multiplying two pieces of individual chords should be equal.  I simply multiplied AE x EC (the labels you can't see very well, sorry,) the first chord, and then BE x ED, the second chord, and they both came out to be 34.36 cm sq.  

In this second picture, I demonstrated that the tangent of a circle multiplied by itself, is equal to the outside piece of a secant multiplied by the entire length of the secant. I squared AB which resulted in 200.77 cm sq, and multiplied AC x AD, which resulted in 200.77 cm sq as well. This proves that the tangent squared does equal the secant length times the outer piece. (~JG2)

Circles in Mega Man II

Whilst playing Mega Man II, I unfortunately died. More or less, this is how I looked right before I did die:

 

All silliness aside, I did notice that Mega Man explodes into a bunch of circles upon death.

The circles Mega Man explodes into when he dies share all of the qualities of circles and can be used to demonstrate them:

For example, these circles can be used to demonstrate Theorem 9-11, which states “when two chords intersect inside a circle, the product of the segments of one chord equals the product of the segments of the other chord.” As shown by my diagram, AX * BX =CX * DX, which is exactly what the theorem states. (~JC1)

And no, Channing, Air Man (pictured below) is not wearing some kind of fancy pants.