Primary Math?

[exchemist]

Hmmm?  What happened to BODMAS - do the brackets first? 

Yes but BODMAS is the rule for simplifying expressions, when you can simplify them. In the case of  √(a² + b²) you can't simplify, because there just is no simpler way to write that expression.  I have explained why there isn't. You should now be able to see this for yourself. 

[hazelm]

This is the whole point of BODMAS - brackets first, addition much later.

 

Look - lets consider the number 5. If you square it, it's 25. OK?

 

Now look at a geometrical interpretation. A line of length 5 units. Square it, and you get a square of side length 5, area of 25.

 

Now look at that 5 as being 4 + 1

 

Squaring it gives (4 + 1) squared

 

Draw your square of side length 5. Mark the position of 4, along the top and down the side. Draw horizontal and vertical lines, and you have a square divided into 4 areas. These areas are 4 squared, 1 squared, a rectangle of 1 x 4 and another of 4 times 1

 

So 5 squared = (4 + 1)(4 + 1) = 4 squared + 1 squared + 4 + 4.....

I got it!  Or, a friend got it and clued me in.  Just as you said.  First add the two squared numbers within the "square root of" symbol and that will take us to the square of the hypotenuse.  And the square roots of each side become obvious.   I wish someone had the keys to type the equation.  My Mac keyboard does have the shortcut ways but I don't have the list yet.  Anyway, it now makes sense.  Thank you very much.  I am beginning to see why Math really is a totally different language from English - or any other spoken language, probably.  Liz Strachan commented that everyone was always telling her how they hated math in school but no one ever said they hated English.  Maybe the answer is stop thinking English when learning math.  :-)

[Turtle]

... I wish someone had the keys to type the equation.  My Mac keyboard does have the shortcut ways but I don't have the list yet.  Anyway, it now makes sense.  ...

I'm not a Macette, but see if this is what you need. > Keyboard Viewer and Mac keyboard shortcuts for symbols

[hazelm]

I'm not a Macette, but see if this is what you need. > Keyboard Viewer and Mac keyboard shortcuts for symbols

That seems to be it but it's quite different from how MS does it.  It is asking us to use the character map which is fine once I get it under my belt.  The computer man will be here tomorrow.  I'll see what he can explain.  Thank you. 

[OceanBreeze]

Just one further thing I think is worth adding

When you see the radical expressed this way:

[math]\sqrt { { a }^{ 2 }+{ b }^{ 2 } }[/math]

There is no need to have brackets around the [math]{ a }^{ 2 }+{ b }^{ 2 }[/math] inside the radical

The bar over the top of the radical is a vinculum:

 

"A vinculum is a horizontal line used in mathematical notation for a specific purpose. It is most commonly used today to indicate the repetend of a repeating decimal. It may be placed as an overline (or underline) over (under) a mathematical expression to indicate that the expression is to be considered grouped together. For most of its uses it has been replaced by parentheses in modern notational style"

 

The vinculum has same order of operations as parentheses.

 

 

[exchemist]

Just one further thing I think is worth adding

When you see the radical expressed this way:

[math]\sqrt { { a }^{ 2 }+{ b }^{ 2 } }[/math]

There is no need to have brackets around the [math]{ a }^{ 2 }+{ b }^{ 2 }[/math] inside the radical

The bar over the top of the radical is a vinculum:

 

"A vinculum is a horizontal line used in mathematical notation for a specific purpose. It is most commonly used today to indicate the repetend of a repeating decimal. It may be placed as an overline (or underline) over (under) a mathematical expression to indicate that the expression is to be considered grouped together. For most of its uses it has been replaced by parentheses in modern notational style"

 

The vinculum has same order of operations as parentheses.

Good point. I was only using brackets because I can't find a root sign with a vinculum on my computer. 

[hazelm]

Just one further thing I think is worth adding

When you see the radical expressed this way:

[math]\sqrt { { a }^{ 2 }+{ b }^{ 2 } }[/math]

There is no need to have brackets around the [math]{ a }^{ 2 }+{ b }^{ 2 }[/math] inside the radical

The bar over the top of the radical is a vinculum:

 

"A vinculum is a horizontal line used in mathematical notation for a specific purpose. It is most commonly used today to indicate the repetend of a repeating decimal. It may be placed as an overline (or underline) over (under) a mathematical expression to indicate that the expression is to be considered grouped together. For most of its uses it has been replaced by parentheses in modern notational style"

 

The vinculum has same order of operations as parentheses.

This is absolutely fascinating and I don't mean what you are explaining.  What came into my mailbox is different from what you have posted at this forum.  However, to add to the mystery, when I clicked "Quote", what appeared in my post here is what is in my mailbox, not what is above. 

 

Let's see what it will show when I click Post. 

[hazelm]

There you are.  Does that make sense? 

[DrKrettin]

What are you talking about?

[hazelm]

What are you talking about?

It changed!  I don't know what is going on but the symbols you typed came into my mailbox differently.  And when I clicked Copy on your actual post, the copy was also different.  But it is now correct.

 

I have just done a copy of my mailbox copy.  Let's see what we get.

 

Just one further thing I think is worth adding

When you see the radical expressed this way:

[math]\sqrt { { a }^{ 2 }+{ b }^{ 2 } }[/math]

There is no need to have brackets around the [math]{ a }^{ 2 }+{ b }^{ 2 }[/math] inside the radical

The bar over the top of the radical is a vinculum:

 

All right.  This is from my mailbox.  Right now it says {math}{a}^{2}+{b}^{2} {/math} .  Sorry.  Something strange is all I can say.  Let it go.

[hazelm]

P S.  It is changing back and forth.  I did copy.paste of how your message came to my mailbox.  I then typed it as it came.  The copy  of yours corrected itself but my typed copy did not.

 

As I said, let it go.  Just something weird going on.  I'll ask computer man about it this afternoon when he comes.  hazelm

Edited June 19, 2017 by hazelm

[DrKrettin]

I don't even understand what you mean by mailbox. Shall we have a nice cup of tea instead?

[OceanBreeze]

I gather that Hazelm has subscribed to this thread and gets email notifications when someone makes a post.

 

I also gather that her email notification does not display the LaTex math characters, instead it displays the LaTex commands.

 

Thus, she sees a difference between what is in her email and what is here on the forum.

 

 

And, the reason why her typed copy of the LaTex commands did not execute is because she used curly brackets around the math and /math instead of square brackets.

Edited June 19, 2017 by OceanBreeze

[hazelm]

I don't even understand what you mean by mailbox. Shall we have a nice cup of tea instead?

Best idea yet.  "Mailbox" = where my mail comes in.  "Inbox"?  Sorry.  Gmail!!!!!!! <g>

 

Tea sounds good.

[hazelm]

I gather that Hazelm has subscribed to this thread and gets email notifications when someone makes a post.

 

I also gather that her email notification does not display the LaTex math characters, instead it displays the LaTex commands.

 

Thus, she sees a difference between what is in her email and what is here on the forum.

 

 

And, the reason why her typed copy of the LaTex commands did not execute is because she used curly brackets around the math and /math instead of square brackets.

Thank you!  I am glad you understood what happened.  Two different softwares that don't talk to each other?  Or two different versions that don't talk to each other?  Whatever.

 

As for the curly brackets, I used those because I thought that was what the original used.  Excuse:  My vision isn't too good any more. So, I misread.  And, no, I promise I will not experiment with that one.  <g>

[Turtle]

Good point. I was only using brackets because I can't find a root sign with a vinculum on my computer.

You have to type out the Latex expression to display the vinculum; it is not a keyboard shortcut symbol. To add to the misery, Latex changes, and the forum software changes, and browsers change (or don't change.)

 

To use Latex I have to flip the little Toggle at top-left corner of the reply/edit box. I also have to do this to format links, but others may not have this problem.

 

At this time, if you see a Latex expression you can put your cursor on it & right-click to get a menu of display options. One of those will show what Hazelm was seeing in the e-mail. This works at this forum as well as other pages where Latex is used.

 

We do have a Latex tutorial thread here, but I can't attest if it covers the most recent Latex version. Good luck & good fun. >> LaTeX Fomulas: Math v2.0

 

To get the entire Latex code to show instead of the Latex display, you have to put code tags around the Latex code.

 

[Math]\sqrt{a^2+b^2}[/Math]

displays [math]\sqrt{a^2+b^2}[/math]

[hazelm]

Ah, the whole thing is explained.  I am allergic to latex. 

 

Seriously, after math, nothing is more confusing to me than these infernal machines.  That is why there are still many pens and pencils around here. 

 

Thank you, Turtle.  I am glad you have the gift.  I shall concentrate on that and see what I can see.   What I gather now is that I pay attention to what is at the forum and not what Gmail shows me.  Right?