This was a fun exchange on Twitter:
I replied that when I lead my trig supplemental instruction session tomorrow and go over the area of a sector, I am going share it like this:
🙂
Shortwave Decibels
“When am I ever going to use this?” has been asked about various parts of math by students through history.
Come on. Admit it. You asked it before, didn’t you? 🙂
Ever used decibels? Then, my friend, you have used logarithms! From ”Understanding Decibels” on The SWLing Post:
dB = 10 log10 (P2/P1)
Okay, you should read the article for more than just that. 🙂
However, just like how we measure earthquakes, hurricanes, and other items that vary by a large range, leveraging powers of 10 to measure signal or sound strength makes a lot of sense. Using earthquakes as an example, would you really want a Richter scale \(10^5\), that is, a Richter scale 100,000 earthquake? Richter scale 5 is so much easier for the brain, isn’t it?1
Although, in the spirit of Spinal Tap’s guitar amp with a maximum volume of 11 versus 10, I suppose I’d love it if when I cranked Shinedown I could tell people I turned it up to 1,000,000. 🙂
Getting back to the mathematics…
Logs are just inverse powers (e.g. \(log_{10} 10^n=n\)). If you do not see a base with your log (e.g. \(log10^n\), then it is the “common log,” which is base 10. [Read more…]
Converting a Weird Polar Graph to a Cartesian One
So, yesterday…yes, Christmas…I proved (or perhaps, better said “derived”) the Quadratic Formula. The fun didn’t stop there. 🙂
My oldest son (visiting for the holiday), seemed to enjoy what I was doing…so I figured I’d blow his mind with how polar equations act in graphs, first showing him a simple \(r = 2\sin \theta\) one. After a bit discussing that, I thought I’d blow his mind more and create the equivalent of \(x = 1\), which is \(r = \frac{1}{{\cos \theta }}\).
Having a brain cramp, I thought I’d shift it one by adding 1 to it (\(r = \frac{1}{{\cos \theta }} + 1\)), but that results in something quite weird. You see, in a \(g(x) = f(x) + 1\) world, \(g(x)\) is just \(f(x)\) shifted up 1. Not so in the polar equation world. 🙂
The green line is \(r = \frac{1}{{\cos \theta }}\). The red lines are what happened when I added one to it (\(r = \frac{1}{{\cos \theta }} + 1\)): [Read more…]
Double Doh! (Spanish Submarine)
One of the problems I have doing math homework is wanting to take shortcuts (get ‘er done). I suspect, however, that it doesn’t save time in the end.
Then, of course there are cases that prove that being meticulous is essential:
“Spain builds submarine 70 tons too heavy after putting a decimal in the wrong place”
And, if that’s not enough…
“Spanish Sub’s New Problem: Once Too Heavy, Now It Can’t Fit in Dock”
Take your time, follow the steps, and check your work kids! 🙂
Proving a Sine Phase Shift from Cosine
I started up college about 4 weeks ago, and in one discussion, a fellow student posited a 90° leftward phase shift to convert a cosine function to a sine one. It made sense, but I told him that without proving it, our professor might come up with an exception.
Well, yesterday on the way to the Denver Zoo (mainly)…
Please remember, I was in a car on varying degrees of bumpy roads. 🙂
(Not that I write well on an iPad Pro screen anyway.)
I’ve grown to prefer using radians over degrees (360° = 2π radians). I hated radians in school.
P.S. I really like the program, GoodNotes, on my iPad for handwriting math “show work.”
Mind Your Numbers by KitKi
Who says math isn’t fun?!
Well, actually, lots of people do. 🙂
However, that just means they haven’t had a chance to play Mind Your Numbers by Kitki. I was lucky enough to learn about the game during its Indiegogo campaign, and grabbed two copies. Good news is it is now available through Amazon, so you can grab a copy. (I actually recommend you get two so you can have up to four players.)
Although it’s just fun to play, it is especially valuable for those trying to help kids with math facts (mutiplication, division, addition, and subtraction). Not only will it exercise those skills, it strengthens stategic thinking. Age-wise, my 10 year-old son, my 23 year-old son, and I (a 53 year-old guy) had a great time…even though I’m not much of a board game guy.
As someone who has tutored a kid who didn’t know his math facts when he should have, I wish I had this tool in my arsenal.
Great work Kitki!