Type quadratic sequence with 1'st and 2'nd difference [Solved!]

X

Hallo Murray

I want to type a quadratic sequence with 1'st difference under and second difference under again. Something like this (I've done it in Word): 

<img src="/forum/uploads/imf-3616-rye.jpg" width="81" height="48" alt="entering-math-graphs-images" />
regards
Rika

Relevant page

<a href="/help/send-math-email-syntax.php">Syntax for ASCIIMathML</a>

What I've done so far

{::}_(\ 92)^238 which becomes `{::}_(\ 92)^238`

X

Hello Rika

It is possible, depending on the processing system you're using (I forget now which one you ended up using!).

The syntax you need is <code>\underbrace</code>

The following syntax works in MathJax:

<code>\underbrace{3\mspace{0.5em}14}{11} \mspace{0.75em} \underbrace{29\mspace{0.5em}48}{19}</code>

This is the result (it's a screen shot):

<img src="/forum/uploads/imf-2251-mathjax-underbrace-output2.png" width="103" height="52" alt="entering-math-graphs-images" />

You can try out MathJax in this sandbox: <a href="http://www.krassotkin.com/toys/mathjax/">MathJax and TeX Dynamic SandBox and PlayGround by Alexander Krassotkin</a>

In <b>CodeCogs</b> (which is a good place to try out more complicated LaTeX, see <a href="https://www.codecogs.com/latex/eqneditor.php">CodeCogs Online LaTeX Equation Editor</a>), it didn't like the "\mspace" bits, but was OK with "\hspace" (both of these exist to give us horizontal spacing).

This worked in CodeCogs

<code>\underbrace{3\hspace{8}14}{11} \hspace{12} \underbrace{29\hspace{8}48}{19}</code>

Here's what it looks like (CodeCogs gives you a downloadable GIF image):

<img src="/forum/uploads/imf-2056-codecogs-underbrace2.gif" width="111" height="36" alt="entering-math-graphs-images" />

Unfortunately, KaTeX (which is what I use on this forum) doesn't support underbrace (yet). Also, there's no plain text equivalent syntax at the moment.

Hope it helps!
Regards
Murray

X

Hallo Murray
thanks a lot. I'm using MathJax. 
I am thinking of offering to become a tutor. But it has been a long time since I've done university Mathematics. I would be able to help up to Calculus 1.
I just checked the MathJax code, and the underbrace works, but not the mspace?
The CodeCogs does not work. Should I put something in the "head" so that it can be recognized?
Regards
Rika

X

Hi Rika

Hmmm... 

(1) That MathJax code worked fine in that sandbox I linked to, and also the official MathJax sandbox (which is the little green button "Try the live demo" on the MathJax home page: <a href="https://www.mathjax.org/">MathJax</a> )

It may be a MathJax configuration issue. You'd need to use one of the LaTex configurations - plain text (ASCIIMath) won't work.

If you don't have any joy, you can always put dots:

<code>\underbrace{3...14}{11} ... \underbrace{29...48}{19}</code>

It doesn't look as good, but it works.

(2) The code I gave does work in CodeCogs. I'm not sure what you are trying to do. If you want to use the image you'd need to upload it to your server and then add it.

The other option they give is to embed some code (see it at the bottom of the CodeCogs editor page).

X

Hi Murray
Quadratic sequences was introduced into our Math curriculum a few years ago. it is the sequence formed out of the sum of an Arithmetic sequence. The learners have to show that the second difference is constant and then be able to obtain `Tn=an^2+bn+c`. I recently found a new way of doing it, without to many formulas and want to explain it.
I can write:
Sequence       = 3; 14; 29; 49;...
1s't difference = 11; 15; 19;... 
2'nd difference =   4;   4;  ....
But it would look much better if there are brackets under each pair of numbers. But i'm not sure if this can be done?

I know how to tell my website that I am using MathJax. What should I put in the "head" section to be able to use LaTex, because I know it quite well?
regards
Rika

X

Murray
I wrote it down and took a picture :}


<img src="/forum/uploads/imf-5015-kwadr-rye.jpg" width="500" height="281" alt="entering-math-graphs-images" />

Regards
Rika

X

Hi Rika

(1) In LaTeX, you would need to make use of \phantom. I played around with that a bit, but the braces overlap each other (under the 14 and 29) and it looks quite ugly.

To get a second row of braces and numerals would be troublesome (not impossible, but I don't think it's worth the effort.)

If you do want to go ahead with that option, the syntax for ensuring MathJax uses LaTeX can be found on this page:

<a href="https://docs.mathjax.org/en/v2.5-latest/configuration.html">Loading and Configuring MathJax  MathJax 2.5 documentation</a>

This one loads everything:

<code>&lt;script type="text/javascript"
   src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MMLHTMLorMML">
&lt;/script></code>

(2) Here's another possible solution for you. I've used a table, and rotated the braces using CSS. I think it's the easiest solution.

<table>
<tr>
  <td>3</td>
  <td>&nbsp;</td>
  <td>14</td>
  <td>&nbsp;</td>
  <td>29</td>
  <td>&nbsp;</td>
  <td>48</td>
 </tr>
 <tr>
  <td>&nbsp;</td><td style="width:20px"><span style="font-size:1.5em;-webkit-writing-mode:vertical-rl;-ms-writing-mode:tb-rl;writing-mode:vertical-rl">}</span></td>
  <td>&nbsp;</td><td style="width:20px"><span style="font-size:1.5em;-webkit-writing-mode:vertical-rl;-ms-writing-mode:tb-rl;writing-mode:vertical-rl">}</span></td>
  <td>&nbsp;</td><td style="width:20px"><span style="font-size:1.5em;-webkit-writing-mode:vertical-rl;-ms-writing-mode:tb-rl;writing-mode:vertical-rl">}</span></td>
  <td>&nbsp;</td>
 </tr>
 <tr>
  <td>&nbsp;</td><td style="text-align:center">11</td>
  <td>&nbsp;</td><td style="text-align:center">15</td>
  <td>&nbsp;</td><td style="text-align:center">19</td>
  <td>&nbsp;</td>
 </tr>
 <tr>
  <td>&nbsp;</td>
  <td>&nbsp;</td><td style="width:20px"><span style="font-size:1.5em;-webkit-writing-mode:vertical-rl;-ms-writing-mode:tb-rl;writing-mode:vertical-rl">}</span></td>
  <td>&nbsp;</td><td style="width:20px"><span style="font-size:1.5em;-webkit-writing-mode:vertical-rl;-ms-writing-mode:tb-rl;writing-mode:vertical-rl">}</span></td>
  <td>&nbsp;</td>
  <td>&nbsp;</td>
 </tr>
 <tr>
  <td>&nbsp;</td>
  <td>&nbsp;</td><td style="text-align:center">4</td>
  <td>&nbsp;</td><td style="text-align:center">4</td>
  <td>&nbsp;</td>
  <td>&nbsp;</td>
 </tr>
</table>

You can use the "Show code" button to grab the table code and paste it into your page.

X

Thanks Murray
I got it!
Want to ask: I am making my website in my home language, Afrikaans. It will be open and free for anyone. May I use articles and pictures from your website and reference to it?
regards
Rika

X

Hello Rika

Yes, you do have permission as long as the original is referenced, with meaningful links.

Regards
Murray