f(t): Help Me With Some Algebra

f(t): Help Me With Some Algebra

Given a chord AB and the intercepted arc S, is it possible to find radius r algebraically? (problem stated at f(t)) The consensus there seems to be no, due to the transcendental nature of sin(x).

But I find it interesting that r could be constructed with a compass and straightedge. However, I feel like I'm cheating with Geogebra since I had to place C in order to draw arc S. So I really wasn't given S; I picked one based on C. Circular logic! (that's a little math joke ... ha ha ha.)

Update: http://www.mathforum.com/dr.math/faq/faq.circle.segment.html#1 Dr. Math has a nice page about solving circles given arbitrary parts. They reinforce the idea that this is a problem with numerical-only solution. Their solution involves Newton's Method, something I myself am not very well versed in these days!


News Media

This XKCD comic reminded me of why I hate most of the News Media. The panel on the left is a pretty accurate rendition of a full screen graphic one of the 24 hour networks had up:

: $170 billion
Bonuses: $165 million

At first glance, one might arrive at the conclusion that AIG was using almost its ENTIRE bailout for these bonuses. "How irresponsible! What an outrage! Despicable!" But upon closer inspection, one notices the difference between the numbers. What if we actually took the difference?

- $165,000,000
= $169,835,000,000

There's $165 million is a drop in the hat. Its about 0.1% of the bailout money. It pales in comparison! It should not be compared. I'm not defending AIG. That's not the issue. The issue is the News Media is presenting information in a misleading format. I also assert the News Media is doing so purposely. They want the outrage, because outraged viewers will watch more. Everything is sensationalized and distorted.

The new propoganda isn't for political gain. The Media wants your viewership and your money. They will distort the facts for it.

Our financial crisis is a result of people misrepresenting information about loans rates, feasibility of real estate transactions, investment options and the market in general. People would bend the truth to gain more money. Now, the News Media is now misrepresenting information... to gain more money. They mimic the actions of the very organizations they codemn.

"Why do we have to take math?" students ask me. Look at the world. Those who understand the system will take advantage of those who do not. A simple concept like orders of magnitude (billions vs. millions) will be lost on many viewers who have been in the habit of non-mathematical thinking.

The next time stats or data is thrown in your face, by the Media or anybody else, pause and think: "what does it really mean?"