Category Archives: Math

Astronomy, Math

“Galaxy Song” with Notes and Alterations

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LyricsNotes
Just remember that you’re standing on a planet ever changing,
Rotating at 1,000 miles an hour		Original: Just remember that you’re standing on a planet that’s evolving,
Revolving at 900 miles an hour

“If you were to hang above the surface of the Earth at the equator without moving, you would see 25,000 miles pass by in 24 hours, at a speed of 25000/24 or just over 1000 miles per hour.”*
It’s orbiting at 19 miles a second,* so it’s reckoned19 miles per second = 68,400 miles per hour.

“Earth is also moving around the Sun at about 67,000 miles per hour.”*
A sun that is the source of all our power“The energy we capture for use on Earth comes largely from the Sun or from nuclear forces local to our own planet. Sunlight is by far the predominant source, and it contains a surprisingly large amount of energy.”*
The sun and you and me and all the stars that we can see
Are moving at a million miles a day
In an outer spiral arm, at 40,000 miles an hour
Of a galaxy we call the Milky Way		1 million miles per day = 41,667 miles per hour.

“Relative to the local standard of rest, our Sun and the Earth are moving at about 43,000 miles per hour (70,000 km/hr) roughly in the direction of the bright star Vega in the constellation of Lyra….”*
Our galaxy itself contains a hundred billion stars“We can only see a few thousand stars at most with our unaided eyes. These are a mixture of stars which are nearby, and bright stars which are further away; but they are only a tiny fraction of the 100,000,000,000 stars in our own galaxy.”*
It’s 100,000 light years side to side“The disk of the Milky Way galaxy is about 100,000 light years in diameter (one light year is about 9.5 x 10^15 meters).”*
It bulges in the middle, 16,000 light years thick“The central bulge is about 16,000 light years thick.”*
But out by us, it’s just 1,000 light years highOriginal: But out by us, it’s just 3,000 light years wide.

“Astronomers estimate that the disk in the vicinity of the Sun is relatively thin—‘only’ 300 pc thick….”*

300 pc (parsecs) = 978.47 light years
We’re 30,000 light years from galactic central point“Of course, the edge on perspective represents the view from the vicinity of our Sun, a star located in the disk about 30,000 light years out from the center.”*
We go ’round every two hundred million years“At this rate it takes us 240 million years to make one revolution around the galactic core.”*
And our galaxy is only one of millions of billions
In this amazing and expanding universe
The universe itself keeps on expanding and expanding
In all of the directions it can whiz
As fast as it can go, at the speed of light, you know
11 million miles a minute,
and that’s the fastest speed there is		Originally, “12 million miles a minute.”

The speed of light is actually about 671 million mph which is 11,183,333 miles per minute.
So remember, when you’re feeling very small and insecure
How amazingly unlikely is your birth
And pray that there’s intelligent life somewhere up in space
‘Cause there’s bugger all down here on Earth

Math

Equations between WordPress, Open Office and LaTeX

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Equations in WordPress

These are the steps to create LaTeX equations on non-WordPress.com blogs.

  1. Install and activate Jetpack.
  2. Connect your self-hosted WordPress blog with your WordPress.com account by going to “Settings” of the Jetpack plugin.
  3. I prefer to use Open Office Writer to type equations. To turn these formulas into LaTeX format, I downloaded and installed Writer 2 Latex. (To install the plugin, I double-clicked two different .oxt files: writer2latex.oxt and writer4latex.oxt. I’m not sure what the difference is, but it seems to work.)
  4. Once you have Writer 2 Latex installed, a “LaTeX” menu item should appear. You can click that and a LaTeX document will appear in the same directory as the OOWriter document you’re working in.
  5. You can then open the .tex file with, as I do, Notepad++ or another text editor.
  6. Alternatively, you can go to a site like this one.

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Finance, Math

How do they calculate what your monthly auto loan payment will be?

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So, I recently bought a new vehicle and was wondering how my monthly payments were figured out. After digging around a bit, I found this site where a high school teacher has posted the formula as an exercise for her students. Not only that, but I stumbled across this other website where I could find simple solutions to the most of my financial woes.

Well, I thought I would share this gem in case anybody else is interested.

\frac{P(\frac{i}{12})}{(1-(1+\frac{i}{12})^{-n})}
 

You can go to this site and the Almighty Internet will give you the same answer.

Alternatively, you can download this document I made in Open Office Calc (free) and see, with your own eyes, what’s going on.

I would love to know, if anyone ever reads this, how the initial finance charge is decided. I thought about it, fruitlessly, until my brain hurt.

Here is the problem:
You have a principal amount of $4049.00. Your finance charge is calculated to be $538.12. Your interest rate is 8.29%. What formula was used to arrive at the value $538.12?

Math, Software, Technology

The I-Pen and Paint.NET for Math

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For anybody looking to make writing out equations on your computer easier, I have two recommendations:

First is the I-Pen (pictured above). It’s plug and play, but I think I had to install software either for my mouse or for the I-Pen itself to make the two device pointers move at two different speeds (you will probably want the I-Pen to move more slowly for greater accuracy).

Second, I have made this blank worksheet for working out problems in Paint.NET. I was using the version of Paint that comes with Windows 7 and it’s quite nice, but I wanted something with greater functionality that would work on my netbook (running Windows XP) as well. So, Paint.NET works well.

The only problem was that I don’t want to have to mess with layers and selecting a canvass size I like every time I need to work through one or a whole slew of equations. So, the above-referenced “blank worksheet” has proven useful so far. I open it once and then each time I want to begin a new equation, I press and hold the “Ctrl” key on the keyboard and tap the “A” key (to select all) and then press the “Delete” key. Voila. Blank math canvass in approximately two seconds.

One issue with this approach is the way that Paint.NET handles layers. In order for my approach to work as intended, the layer settings window must look like this:

However, quite annoyingly, when you close and reopen this saved document, the layer settings window looks like this:

So, it must be changed back each time to allow trouble-free math drawing.

Math

Finding Reciprocal Functions SEC, CSC, COT on TI-30XA

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First, you may want to refresh your memory of the regular trig functions:

Now, let’s find \csc \frac{5\pi }{4}.
If we look it up on WolframAlpha, we find that it equals -\sqrt{2}, or, roughly, -1.4142.

To get this answer on the TI-30XA, first remember that \csc is equal to \frac{1}{\sin }.

So, what we’re looking for could be expressed as \frac{1}{\sin \frac{5\pi }{4}}. Once we know this, we can type 5\cdot \pi into the TI-30XA.

This gives us ~15.7. (Make sure you’re in radian mode. If not, press the DRG button — located by the 2nd button, upper-left — until you see RAD appear in small letters on the screen.)

Now, we can divide 15.7 by 4. This gives us 3.925. If we take the \sin of this (by pressing the “sin” button while 3.925 is displayed), we get -0.7. IF we divide 1 by -0.7, we get -1.43. As you can see, this is close to the correct value. You can get a more exact value by using the STO function on the calculator. [Press “STO” while a number is displayed on screen and then the number “1” on the keypad. Press the clear button (ON/C). Now, press RCL and the number “1” on the keypad. Your saved value should appear.]

Math, Psychology, Statistics

Statistics Miscellanea

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Formulae Quizzes (use the learn feature): one, two

T test
—t Table
—t value calculator
—reporting results of repeated-measures t test example: Changing the background color from white to red increased the attractiveness rating of the woman in the photograph by an average of M = 3.00 points with SD = 1.50. The treatment effect was statistically significant, t(8) = 6.00, p < .01, r2 = 0.818.

ANOVA
—One-way Formulae
—Critical F Calculator

Correlation
—Pearson Correlation Computational Formula Worksheet
—Pearson Correlation Definitional Formula Worksheet
—Critical Values for Pearson Correlation

Chi-square
—Chi-square Critical Values

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