Understanding Electronics Basics #2

[Muttley600]

But surely if you had centres 2∏ apart you are left with what looks like a gear cog inside out unless you have the right size for a circle, which our milling machine went to about 2.5" unless used with rotating base, making life far simpler as you could use a smaller bit

Happy to work in radians or degrees but can see why people use radians for ease of equation


Reading onto equation, are you saying it is possible to do it via sums & not end up with teeth on inner circle.eek

Now you have got my Interest purely on the curiosity front alone

Thanks for speaking plain english & not hiding behind fancy names & I take it you were being sarcastic about the teacher but am somehow relating me using calculator to get sine?

Trusses are a whole different skill level completely, you do really need to know your stuff then unless your good with a pencil & like heights

Today has flown by, new chap picking things up well, I can feel my life is about to get slightly easier instead of me trying to do three jobs, two I can manage, three was getting silly.lol

Hope your both having a good weekend

 

[KeepItSimpleStupid]

I think you misinterpreted. Here is an example of a bolt circle on a flange: **broken link removed**

The question was how to drill the holes, not make the round flange on a mill.

If you had 8 holes then each hole would be n * 2* ∏ * / 8 apart
1st hole 2∏/8
2nd 4∏/8
3rd 6∏/8
.
8th hole 2∏

Remember the 2∏/8 etc is an ANGLE in radians.



If they were on a 4" RADIUS then x=4*sin(2∏/8); y=4*cos(2*∏/8) etc. All assuming the origin (0,0) is the center of the flange.

Noticed it depends on how you count: either 0 through 7 or 1 through 8.

 

[Muttley600]

I was misunderstanding, I can see we need holes 0.25∏ around the radius
Then the sine & cosine are the measurements of the hole from 0-0 that pinpoint the location to drill
I just need the time to see how the sum is working now, not much time at the moment

 

[Muttley600]

1st hole 2∏/8
2nd 4∏/8
3rd 6∏/8
8th hole 2∏
Remember the 2∏/8 etc is an ANGLE in radians.
If they were on a 4" RADIUS then x=4*sin(2∏/8); y=4*cos(2*∏/8) etc. All assuming the origin (0,0) is the center of the flange.
Noticed it depends on how you count: either 0 through 7 or 1 through 8.

All this makes sense

If you had 8 holes then each hole would be n * 2* ∏ * / 8 apart

but this I can't see? n*2*∏*/8

Broken down: hole times two times radians times divided by eight

what is that saying, I can't see why the red bold is there, & the black bold is cancelling out divide surely?

if you can tell me that I just need to spend this m0orning updating my folders into some kind of order then I'll go back to log of 55

 

[cowboybob]

He's saying that the "quantity" [LATEX=]\frac{2*\prod}{8}[/LATEX] is multiplied by n, as in this formula: [LATEX=]n*\frac{2*\prod}{8}[/LATEX] or, if you like, [LATEX=]\frac{n*2*\prod}{8}[/LATEX].

 

[Muttley600]

He's saying that the "quantity" [LATEX=]\frac{2*\prod}{8}[/LATEX] is multiplied by n, as in this formula: [LATEX=]n*\frac{2*\prod}{8}[/LATEX] or, if you like, [LATEX=]\frac{n*2*\prod}{8}[/LATEX].

Man, I'm really struggling with the math, I can't see past your middle example but as n= not n* which is just highlighting my lack of knowledge on the math front, I've got to learn more otherwise I'm just going to keep struggling


On a lighter note, I've had to reorganise my folders as attached as the math was merging into understanding of components, this will highlight how basic my understanding is thus far, I'm going back over everything as I feel the meaning of words is my biggest trip, I know we have covered stuff, just to need to put it somewhere easy to hand as a guide when it is brought up until I get used to meanings, then I need to nail better understanding of the math

 

[KeepItSimpleStupid]

The formula in the attached is off. The 2*pi/n/n heading should be 2*pi*n/8. The attached is a little goofy because Excel had trouble and the axis aren't quite symeteric, but you should get the idea,

 

[cowboybob]

OK.

I can't see past your middle example but as n= not n*

Multiplication is often "implied": by that I mean certain math functions are eliminated from a formula to "clean it up", or "make it less busy". Doing so does not change the meaning of the formula.

In this case the times symbol is "understood", for example:

[LATEX=]2\prod[/LATEX] is understood to mean "2 times ∏", or "2 * ∏" or, lastly, "2(∏)". ALL three examples mean the exact same math function is to be performed. Of the last three, all were "reduced" to the simplest form of "2∏".

In "Basic Understanding..." doc., in the Batteries... paragraph:

you cannot connect them in parallel but you can in series

No. You can connect them in parallel. It is best to do so, however, with batteries of equivalent" potential since if they are of differing potentials, the greater will lose potential (and possibly start a fire) as it loses energy through the lesser potential, until they are equal.

Resistors:

Example:Series/Parallel Network

The current arrows (for what ever reason(s), are reversed.

Resistors:

Resistors alter the V by limiting "I" as a load & dissipates excess "I" as heat and voltage (my addition).

"Meaning of Words.Doc":

Fine.

"Algebra Learning.Doc":

Fine.

 

[Muttley600]

A big thank you CBB
I was thinking the * suddenly appearing meant it changed something, so my understanding is fine, I'm just not used to *
Thanks for looking over attached, a bit basic I know but I had to start somewhere

 

[KeepItSimpleStupid]

Graham: We are heading to an explanation of the "complex Impedance Plane"
CBB:
a)See if you can fix Graham's version of Power in the Algebra doc. e.g. add powers of 10, power of 2.
I don't think his explanation is quite right.
b) Also see if you can explain unary minus. The latter there as been an extensive discussion here that you have to check. The order of operations, you generally don't, but you still have to check. e.g. -2^2 This always causes grief. Excel evaluates it to 4 and Wolfram Alpha evaluates to -4.

 

[cowboybob]

KISS,

Ok.

Didn't read that one all that closely.

 

[KeepItSimpleStupid]

We went over times being "*", "x" and ()() and the fact that it can be explicit and implicit long ago. CBB just did another explanation of say (1/x) *x etc. You spent a fair amount of time with that concept.

The same with "x**n" and "x^n" and [latex]x^{n}[/latex] all mean the same thing. I'm lazy as to which I choose to use here.

While we are here, I'll introduce another mathematical operator, the "!". This is called a Factorial. 2! is 1*2, 3!= 1*2*3 and 5! = 1*2*3*4*5
This operator is rare, but it does show up in probability and when discussing infinite series. Th 2! would be called 2 Factorial.

 

[cowboybob]

Also see if you can explain unary minus. .... e.g. -2^3 This always causes grief. Excel evaluates it to -8 and so does Wolfram Alpha.

Assuming we're not considering it's usage in computer programming languages:

Graham,

The "-" sign can have several meanings, two of which are:

1. "Minus"
2. "Negative".

In the following simple formula, both meanings are displayed:

[LATEX=]8 - 10 = -2[/LATEX]


i.e., we would say the formula as: "eight minus ten is equal to negative two (and I suppose you could say "minus two, as well, but for the sake of the argument, let's stick with "negative" two).

Now, of course, a number that is being multiplied by a - (use "minus" in ths case) obviously has a different connotation.

Let's start by stating a simple math assumption: ANY number, when multiplied by 1, is essentially unchanged. OK?

If, however, we were to multiply a number by -1, it does what?

It changes the "sign" of the value, making a considerable change to its value, right?

So, take, for instance as KISS offered in the quote above:

-2^3, which could (and should) be read as "negative two raised to the third power"

OR [LATEX=]-2^{3}[/LATEX] OR [LATEX=]-(2)^{3}[/LATEX].

OR, read as "negative one times the quantity two cubed, then [LATEX=](-1)(2)^{3}[/LATEX] OR [LATEX=](-1)*(2)^{3}[/LATEX].

One last example (YEAH!!!)

It can also be written as -2 times -2 times -2 = -8: (-2 *-2 = 4, then, -2 * 4 = -8).

These are all identical in their solution.

I know. lotta verbiage for what is trully a simple concept, but with a slew of options in how to write or express it - welcome to mathematics. Being able to wade through the myriad variations is no small task and only becomes "bike riding" (you never forget how) with practice.

 

[KeepItSimpleStupid]

CBB: A moment ago, I changed my example. The points are: a) the example was bad; b) Excel and Wolframalpha evaluates (-2^2) it differently

 

[Muttley600]

This all looks good, looking forward to getting my head around it all

So we have the cartisean plane broken into 4 segments as per KISS's attachment, now numbers have lots of different names, does each 1/4 have different named numbers I.e. - (read minus) whatever have different name to 3?
Or is it simply 3 is a whole number & 0.456 is a complex number
I think we've covered this so I need to finish going over what we have covered but thanks for explaining how things can be put differently, I got the house roof & - was simply -2000 (edit: ignore me, im tired.lol, ok, -8) but seeing the operations helped lots

That factorial thing doesn't make sense yet but I'm sure it will

 

[Muttley600]

Do you know, that suddenly made sense why the * is there, it is to do with exponent/power of, now I get it

Time to go home, back on in a bit

Should get really good at math then, looking forward to it being as easy as bike riding cause it seems electronics is made up by numbers, so lots of chance to practise

 

[cowboybob]

The latter there as been an extensive discussion here that you have to check. The order of operations, you generally don't, but you still have to check. e.g. -2^2 This always causes grief. Excel evaluates it to 4 and Wolfram Alpha evaluates to -4.

KISS, I see what you saying, i.e., does it mean [LATEX=] (-2)^2 [/LATEX] OR [LATEX=] (-1) * (2^2) [/LATEX] ?

Googled Wolfram Alpha as I had not heard of it. Then googled "Wolfram Alpha Exponantial Funcion" and got this:

View attachment 63223

So I can see a relationship to sine and cosine in the graphs. But I've got to be honest, I don't have a clue why this math engine would give us the -4 answer to the -2^2 problem.

And I'm not sure I want to know. Am I wrong in assuming that this is a "new" way to determine the sine of an angle, (Honest question, here. You math skills are obviously superior to mine) or did I sleep through that lesson all those years ago?

Graham,

Your "Power of 10" exponent example in "Algebra.doc" needs re-thinking and re-writing:

View attachment 63224 ("When using whole numbers..." sentence)

The sentence should read something like this:

"When raising the number 10 to some exponential power, the exponent can be considered to represent the total number of zeros shown after the number 1."

That way the examples make sense.

That may have been what you meant, but it was not what you wrote.

Nit-picky? Yeah, but math will make you that way.

 

[Muttley600]

This isn't bad too:

Neither is this: https://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=3495&pf=1

WOW!!!!!!!!
This is brilliant, I can't remember the last time I wanted to carry on reading while trying to keep my eyes open
I'm totally absorbed in this, just got to part where it is showing how sine is worked out
Fascinating

 

[Muttley600]

But -2^2 does equal -4
I thought you were working on -2^3 which does equal 8

Surely as follows:
-2^1=-2
-2^2=-4
-2^3=-8
-2^4=-16

Now your going to tell we've moved on & by adding - we get a different answer aren't you.lol

 

[Muttley600]

That may have been what you meant, but it was not what you wrote.

Nit-picky? Yeah, but math will make you that way.

It was what I meant
Feel free to correct me, rather get it right

I need coffee to keep awake.lol