Intmath Newsletter - Length of an arc, what’s new, goals

By Murray Bourne, 07 Jan 2010

Happy New Year to everyone!

In this Newsletter

1. What's new on IntMath; and plans for 2010
2. Math tip – Length of an arc
3. Subscribe, connect & communicate with IntMath
4. Latest from the Math Blog
5. Final thought – Goals

1. What's new on IntMath

(a) Math graphs without images

Need to draw the graph of a function?

I've added some new pages where you can see math graphs using scalable vector graphics rather than images (like .gif, .jpg or .png). You'll see a different graph each time you load the page (not like images, where it's the same each time you see it).

  • Adding vectors: This page in the Vectors chapter produces a different example each time you re-load it: Adding Vectors.
  • User-generated graphs: You can plot your own math graphs on this page: Plot your own SVG Graphs

[Please use Firefox, Chrome, Safari or Opera browsers. Internet Explorer requires Adobe's SVG Viewer plugin for this to work.]

(b) Faster IntMath

Slow-loading Web pages irritate everyone. I did some tweaks so that all pages on IntMath load faster. I hope it improves your enjoyment of the site!

(c) New in the Newsletter

When you subscribed to the Intmath Newsletter, I gave you an opportunity to indicate the topics you'd like me to cover.

Well, the list of requested topics is now very long (several hundred topics!). I can't cover them all, but I'll do my best.

Also, there is quite a broad range of people reading this Newsletter. Most are students, some of whom are beginners studying algebra, while others are doing more advanced topics, like trigonometry, logarithms and graphs, while others are studying calculus.

My attempt in each Newsletter is to cover a broad range of topics and hopefully you find something interesting in each one.

For future Newsletters, I'll still aim to have 2 Math Tips, with the first one being more "general" in nature and applicable to just about anyone at any level of mathematics; while the second one will be aimed at those of you who have been studying math for a longer time.

(d) Plans for 2010

I have lots of interesting new things in store involving IntMath during 2010. Watch the Newsletters for announcements!

2. Math tip – Length of an arc

A reader who works for a glass company (true story) wrote to me recently and asked how to solve the following.

I've got to make a window with a curved top. The width of the frame is the same all round, including the part around the curved portion.

What's a formula for the length of the inner arc of the curved portion?

The required length is labeled HI in the diagram.

window with curved top question

(This is not quite a "Norman window", would have a complete semi-circle on top.)

This is a typical "real life" question, in that we don't have a lot of information to go on, so we'll need to make some assumptions.

Try it yourself first. The solution involves trigonometry and the use of radians (a better alternative to degrees).

Then check out the full solution.

3. Subscribe, connect & communicate with IntMath

Here are a few ways to keep up with the latest on IntMath:

  • Subscribe to the blog so you are alerted every time there is a new article. (you can use the blog feed in your iGoogle or MyYahoo page).
  • Get the "daily Math Tweet" on Twitter: IntMath on Twitter
  • If you want to connect with me on Facebook, please say you're a subscriber to the IntMath Newsletter. Otherwise, I won't know who you are.
  • I love to get your feedback. You can comment on any article in the blog or ask your questions in the Comments section in IntMath..

4. Latest from the Math Blog

1) New names for the days of the week

Perhaps it's time to move away from the ancient names used for the days of the week?

2) Classic math mistakes

Displaying posters of math mistakes can actually help students to learn.

3) Friday math movie - Pump up your brain

Looking for a sure-fire way to boost your math scores? Check out this video that helps you to pump up your brain.

4) Fair slicing of the pizza - using math

Not all pizza gets sliced neatly through the middle. How can we ensure a fair distribution of slice area?

5) Friday Math Movie - the Web's secret stories This is one artist's visualization of the emotions of the Web.

5. Final thought – Goals

The beginning of a new year is a good time to reflect on what we achieved last year and what is in store for 2010.

There are 3 types of people. Are you one who:

  • Makes things happen?
  • Watches things happen?
  • Wonders what happened?

In every math class, there are those who ensure their learning is efficient and enjoyable. They make it happen by being organized, reading ahead, listening in class and practicing what they learned before it fades away.

Then there are those who regard math as a "spectator sport" and let the teacher do all the work — then wonder why they aren't doing very well.

Finally, there are those who have no idea what is going on. They are easily distracted and have no idea how to answer if they are asked a question.

So what are your math goals for 2010? Will you be someone who makes things happen and therefore improve your chances for success?

Until next time.

See the 7 Comments below.

7 Comments on “Intmath Newsletter - Length of an arc, what’s new, goals”

  1. Khan says:

    In practical life, math finds little application. Do you agree?


  2. Murray says:

    Hi Khan. Actually, this blog is largely about helping people see how math is used in "real life". Do a search here on the blog for [real life] and you'll see some of the things math is used for.

  3. ahmed says:

    The article :Length of the ARC " is an excellent example for all of us that one must be in contact with the small things,the practical matters as well as advanced topics and theory

  4. april says:

    well, do you agree that, " math is not hard as you think. It's harder,eh".

  5. hailegwergsah says:

    first of all i want like to say thanks so much more for your
    help me as well as for others, i would like say
    if possible I want ask some hyper mathematics books of 1,differential equation
    2,number theory
    3,complex number
    4,linear algebra
    thanks for your assistance

  6. Murray says:

    Hi Hailegwergsah. Perhaps the Open Courseware from MIT will help?

  7. DILLI PRASAD says:

    It is appreciated work for us .First congratulation for
    your work.keep up it.

Leave a comment

Comment Preview

HTML: You can use simple tags like <b>, <a href="...">, etc.

To enter math, you can can either:

  1. Use simple calculator-like input in the following format (surround your math in backticks, or qq on tablet or phone):
    `a^2 = sqrt(b^2 + c^2)`
    (See more on ASCIIMath syntax); or
  2. Use simple LaTeX in the following format. Surround your math with \( and \).
    \( \int g dx = \sqrt{\frac{a}{b}} \)
    (This is standard simple LaTeX.)

NOTE: You can't mix both types of math entry in your comment.

Search IntMath, blog and Forum