PB Algebraic expressions

[Cliff Nichols]

This may not be the right forum (and if not could someone tell me how to move the topic, or admins move and tell me where) to ask this question and it all boils down to basic math that I know, but with a small twist.

So I wonder...

1. What key word should I look for in the docs for what I am sure is built in already for some algebraic equations
2. Some examples?

I will try to draw and explain below what I am after if I can draw it

     ___________________________          -|
    /  |                       |\          |
   /   |                       | \         |--- Height
  /    |                       |  \        |
 /     |                       |   \       |
/      |                       |    \     -|
|      |                       |     |
|      |                       |     | 
|Ramp1-|--------Travel---------|Ramp2|-----
|      |                       |     |
|                                    | 
|--------------  TOTAL  -------------|

Typically Trapazoid = (1/2 Ramp1) + Travel + (1/2 Ramp2)

Formula = Ramp1 + Travel + Ramp2
where:
	Ramp1 = Time1
	Travel = Time2
	Ramp2 = Time2

so:
	Ramp 1 = 1/2 total ramp up and down
	Ramp 2 = 1/2 total ramp up and down	
	Travel = what is left over

I can hardcode the math for this if I need, but the one thing that I can NOT remember (yeah been too long for basic math for me, so I thought I would ask), is if Ramp2 <> Ramp 1....is the formula still 1/2? or a ratio thereof?

For example:
Ramp1 = 2 seconds of total
Ramp2 = 6 seconds of total

Do I still use the age-old formula? or do I change fractions so the ramp 2 is visually and mathematically longer than the original?

This is particularly hard for me to explain, so I hope you get what I meant from the description above?

[Paul Dixon]

Cliff,
It looks like you're after the area under that shape in which case it's:

Total Area = the sum of the 3 areas, height*ramp1/2 , height*ramp2/2 , height*travel

= height*(travel+ (ramp1 + ramp2)/2).

It doesn't matter that ramp1 and ramp2 are different. The area of the triangle is 1/2 * base * height. Height is as given, 1/2 is a half and the base for each of the triangles is ramp1 and ramp2

Paul.

[Rodney Hicks]

I'm not entirely sure I understand what you're after but it looks to me like you want distance not area. If I am correct the formula would be ramp1=square root of the sum of the squares of the width and height, and ditto for ramp2.

[Cliff Nichols]

Thanx guys,
That verified what I was fairly certain of that the area of a Triangle is always (1/2) * base * height, irregardless of 1 triangle base may be larger than the other base.

Sorry I had to ask a question like that, but just needed verification of what I may have brain-cramped on in math I have not needed to use for years.

[Mark Hunter]

(Mathematics questions usually go in the Programming forum.)

You can always take the triangle and slice it into horizontal slivers, then slide the slivers to one side so you have a right triangle. It’s half a rectangle with the same base and height as the triangle.

I think this is an application of some guy's principle. Cavalieri ? Yes, just looked it up:
http://www.jimloy.com/cindy/cavalier.htm

[Cliff Nichols]

I got it running, once I realized from lack of practice, that the simple geometric calculations hold true...
my confusion was mostly due to lack of practice, and wondering if I forgot one
thanx again guys for the lil kick in the head I needed to verify what for me was "Lost Knowledge" was not as lost as I 1st thought it was