# Calculator Worksheet (2)

I've added a second calculator worksheet to the Handouts page. It's targeted at students who are at precalculus level since knowledge of fractional exponents are required. Of course, you can modify the $\LaTeX$ code so it will be appropriate to your level.

# Problems: special right triangles

I've added another problem to the Problems page.

Using your knowledge of 30-60-90 right triangles, prove that the area of an equilateral triangle with side of length $s$ is given by $A=\frac{\sqrt{3}}{4}s^2$. Use this formula to find the area of a regular hexagon with sides of length $s$.

# Odds and Ends: April 19, 2013

Two items that might interest you:

First, I mentioned online LaTeX compilers in this post. Those compilers are great for math teachers (or anyone) who uses multiple computers, especially computers where they lack administrator rights. A year later and I've come across a new online LaTeX website  which looks better than anything else. It's called writeLaTeX and there are many reasons you really should take a look:

1. It's free! Just go there and start typing.
2. It's simple to use. The diagram says it all.
3. There are templates provided for creating a paper, presentation, and more!
4. As you type, you're given a "rapid" preview of the changing document.
5. If you sign up for writeLaTeX then you can collaborate with others on LaTeX documents.

When you go to the website you'll see 2 buttons: one to create a new paper and the other to create a new presentation. But if you look a little further down there are links for a "WriteLaTeX Tutorial", "Templates and Demos", and "Sign up for a free account". Clicking on "Templates and Demos" will take you here, where you'll find you actually have access to 3 pages of templates. Even better, writeLaTeX is available for your I-pad, tablet, and mobile device.

I spent some time experimenting with it and found that the "rapid preview" was not so rapid on my machine. Gummi, the IDE I use in creating many of my posts, updates much more rapidly than writeLaTeX. This, however, I think is a minor issue. writeLaTeX looks to be a useful tool every math teacher should be aware of. I've added a link to writeLaTeX on the sidebar.

Second, there is a good article on "Academias Indentured Servants". Though it isn't directly related to high school math, it does relate to an earlier post where I mentioned the pool of qualified people who could teach at the high school level if it weren't for the certification requirements. Of course, not every adjunct professor would be suitable to teach at the high school level (eg failure to pass a background check) nor would some want to teach at the high school level. But, having seen this situation up close, I also know there would be a decent percent that would abandon the poverty wages of academia for a high school teaching job--if only those onerous certification requirements were removed.

# Sage Interact: trigonometric transformations

The screenshot above illustrates a new manipulative I've put together, running on the Sage Sandbox page, that let's user explore transformations of the trig functions sine, cosine, and tangent. More specifically, the user can experiment with how the values of A, B, C, and D affect the graph of:

1. y=Asin(Bx+C)+D
2. y=Acos(Bx+C)+D
3. y=Atan(Bx+C)+D

Two issues came up along the way:

1. How do you control the range of y-values in the output?
2. How do you make tangent plot as a disconnected graph?

I've added information to address these topics to the Sage Interact Essentials page. The code for the manipulative can be found on the Python/Sage page.

# "Proof": the real numbers are uncountable

In an earlier post, I gave my opinion that the most important lesson of high school math should be that the rational numbers have measure 0. As part of that mission, the rational numbers were ordered in this post. Today I've added the "proof" that the real numbers aren't countable to the Handouts page. No doubt some of you have seen it before but it's rot really a proof unless you've established when two different decimals represent the same real number. Clarifying that issue, unfortunately, makes a real proof too difficult so you're best off asserting that mathematicians have proven this to be true. I've given a sketch as to why that's so as well in case you get asked. By focusing on the "proof" (rather than proof) that the real numbers are uncountable it's within the grasp of an accelerated math class.

# Odds and Ends: March 28, 2013

An earlier link (Chessville) is no longer any good so I've removed it and added 3 new links you might find useful.

1. Online Scientific Calculator links you to a web based calculator for some "quick and dirty" calculations.
2. PiCalc is another online scientific calculator.
3. 3D Function Plot is a link to a very nice graphing calculator (shown above). It does almost everything: 2D plots, 3D plots, parametric plots, contour plots, gradient fields, pie charts and more. This site is especially nice because not only do you have a lot of control over how things are plotted but you can also download your plot in a variety of formats including, but not limited to, eps, bmp, gif, animated gif, tif, jpeg, and pdf. Note that images created on the website should be cited if you're using them in publications.

I plan to see which online calculator link (link 1 or 2) is more useful and remove the other. Got a favorite? Let me know.

Finally, the tournament to determine a challenger for the next world championship is winding down and it's a 3 horse race: Carlsen, Aronian, and Kramnik. No real surprises here as these are the top 3 players in the world according to the Live Chess Ratings. There's been some good fighting chess and if you haven't seen the Svidler-Grischuk game from round 9 then you're in for a treat. Remember, you can follow the games live on ChessBomb (the link is on the sidebar) and there is streaming commentary from the official tournament site.

# Sagetex: Randomized Test with Answer Key

Once you've gotten over the initial learning curve of working with Sage, sagetex, and $\LaTeX$ and created your first randomized test template you'll be able to copy and paste code from your working template to create additional tests/quizzes quickly and easily. But there's a huge added bonus: you can program Sage to create your answer key.  In order for Sage to generate the answer key correctly, though, you'll need to make sure you've converted the Python integers created by randint() to Sage Integers using the Integer() function as discussed in the previous post.

To help you along I've put together a simple template for a randomized test to help you. In order for it to work, you'll need to have Sage installed on your computer. The process for creating a document using sagetex is covered here.

I've put the file, called SageTemplate, along with the output on the Handouts page. Of course, since the test is randomized my output will almost certainly be different from your output. It's there to give you a look at the final product and an incentive to install Sage onto your computer.

# The Best Free Ipad Calculator Apps

Linux is the best operating system, period. Unfortunately, this well kept secret means you'll be forced to work with some other operating systems along the way. Schools (including my own) have latched onto the Ipad as the tool of choice. So it's good to know what apps are out there. I've selected the free calculator apps that I like best. I don't include the Sage app because it requires you to be online and the input is clumsy on tablets. My calculator choices are all scientific calculators because a plain vanilla calculator won't be able to handle a variety of basic high school math calculations. Here's the list of the best calculator apps out there.

4. Free Graphing Calculator is a good quick-I-need-the-answer-to-this-simple-calculation calculator. Although you have the ability to for more complicated calculations, such as hyperbolic sine, it's cumbersome to use. On the positive side, it allows you graph multiple 2d functions simultaneously and gives you access to mathematical results. Can't remember that half angle formula? Not to worry, this calculator has it.

3. HiCalcHD comes in next but the annoying reminders when you start it up detract from the experience. A large variety of functions are readily available, including trig functions, log functions, exponentials, factorials, combinations, integrals, and series. Some of the nonstandard calculations tell you how to properly input the calculation you are working on  (such as the definite integral) while you're typing. You can even set the calculator to work in RPN (reverse Polish notation). Great calculator but those reminders....

2. Calculator $\infty$ is free for now, so download it ASAP. No really. Stop reading and download it now. This calculator has everything HiCalcHD has and even lets you input fractions and convert the resulting answer to a fraction.

1. Halcyon Calc Lite takes top spot, though it is definitely not for everyone. Pictured at the top of this post, it's modeled after the HP28S calculator: a calculator that was cutting edge when I bought it over 25 years ago (!):

Since I own the HP28S and am familiar with RPN notation it was pretty easy for me to find my way around. There is more functionality here than any of the other calculator apps I've mentioned, probably more than a typical person will use. Unfortunately, someone new to this type of calculator will almost certainly struggle.

I do have one complaint, though. After graphing a function I was unable to figure out how to get back to the calculator. I couldn't find instructions anywhere. When I exited the app and opened it up again, I was left looking at the graph I created. Eventually I just deleted the app and installed it again. Whether that's a bug, lack of documentation, or a feature meant for the paid version, I have no idea. Note there's a demo video on their website, if you're curious.

If you need an excellent scientific calculator then Halcyon Calc Lite (for people who want RPN) and Calculator $\infty$ (for people who don't) are the best free apps out there.

# Odds and Ends: Feb 24, 2013

Sage 5.7 was released recently. The changelog is here.

I've added 2 links to the sidebar: ChessBomb is a great website for following top chess events. They provide real time chess analysis with a computer engine. It's all free, but if you're willing to register then you'll get even more features. With respect to LaTeX, I've finally gotten around to adding a link to TUG (Tex Users Group).

I've added information to the LaTeX page: a link to free PDFs on PSTricks and on the Sage Interact Essentials page there is now a link to the colors that can be referenced by SAGE.

Some websites that are worth a look: Online Schach Analyse for online analysis of chess positions. Several engines are available. Perhaps a convenient tool if you are on the road with no access to a chess engine? Math-Fail.com has a Happy Face Cheat Sheet you might find amusing.

# LaTeX: Generic Test Template

I've added a generic test template to the Handouts page. Here's a screenshot of the first page; click on it to enlarge.

Notice in the code that the code has \documentclass{exam}, rather than article. You can download a PDF with more information on the exam class here;  using it makes test creation a little bit easier. I like the answer lines which save you from having to hunt for that final answer.

I've used the fix-cm package to make the fonts larger: students complained that the traditional default size fonts were too small. There's even an included a section for the answers which you might not appreciate for now but it will be very useful, however, when  the sagetex package is added. I thought a generic template (without sagetex) would be useful for those who didn't need the power of Sage in their documents.

The template has 3 inputs: the course, teacher name, and title of the quiz/test. You can see that information in the red box below:

Modify the information to include your math course, the title of your quiz/test and your name; it will appear at the top of every page other than the first. I debated about including the course information on the first page but found in my particular case that having the class period was more important.