@Carl Love 

About the formula defintion for the chord section : 

 "The final result for the area must include arc-functions" 

For me it is not direct clear why is that arcsin appears in calculation : it is a angle in radians
If the final reslut has used earlier arcsin result , yes then it goes further in the calculation: make this sense ?  

@tomleslie 

Thanks

I will study examples of this in my worksheets tasks again and using help ( elementwise).
I reread post from you too ( its not possible to link this post here? : a handy feature of a forum)

Ah yes it can be linked of course https://www.mapleprimes.com/questions/229763-Righthand-And-Midpont-Rule-For-Riemann-Sums-#comment269722

Another useful comment about he likewise ~operator

@janhardo 

Some things are left:

- return display  : when using this ?

- role of [ ] in 2 examples ?

yv:=unapply( f, indets(f, 'name') [ ] )~(xv);   

plot
                            ( f,
                              indets(f, 'name') [ ] =a..b,
                              color=red
                            ),
- p,L:=approxL( f, a, b, N):    p, L  ?  

@tomleslie 

Looking again to the code.

I aspected that yv  -values of f  should be stored in a array, but that happened here.

yv:=unapply( f, indets(f, 'name')[])~(xv);

But there is not Array made for this at forehand , well perhaps it has to do with the  ~ (xv) operator
It depend then from what datacontainer type( source container)  is used by ~(xv) ?

In this case it was a Array ,but was it a list then you get probabably a target datacontainer  list?   

Its s strange symbol [ ], it can also used as a range ? [ ]= a..b

plot
                            ( f,
                              indets(f, 'name')[]=a..b,
                              color=red
                            );

Than there is also return display   why is this ?

The procedure is p, L: = approxL( f, a, b, N):  were stands p, L for ?

So i am unsure about the [ ] used to free a variable from a set  and used a range [ ]=a..b

And unsure about the ~ operator about source datatcontainer to target datacontainer

@tomleslie 
Thanks

Very helpful.

Seems that [ ] is used for {x} to get into x  for the right function definition
Its a good idea/approach  to strip elements of the commando and to see what it actually does with the outcome.  

 

@Carl Love 

This basic derivation for a chordal segment there is used arcsin why not  sin ? 
Makes it difference in a calculation.

Its is more userfriendler to use in calculation degrees , and the central angle is measured in degrees in the basic derivation. 

@Carl Love 

I am trying to figure out further this command

So the command yv:=unapply( f, indets(f, 'name')[])~(xv) basically means

1. figure out the name of the idependent variable in the expression 'f'
2. Using 'f' and the name of its independent variable, convert these to an appliable function
3. Apply this function to every element in the container 'xv'

yv is now  a Array filled with y-values of f  , its construction of yv to a Array is by using [ ]  
Using this  [ ]  how ?  

@dharr 

The plot is showing the right result, good.

Takes a lot of time to proof geometrical results in Maple, but its no problem   

@dharr 

Thanks

Using the geometry package for confirming results in geometric expression
Why there is not something in Maple like geometric Expression ? 

@Carl Love 

Thanks

Interesting, because maybe you has used a instant formulae for the chordal segment, but that is not the case
Highlight is the formulae, but what is so special on this formulae ?

@Carl Love 

Thanks

Its clever too , more then the other example

Using a circle segment seems to be the fastest way., but the code is more advanced then the other example.
That makes it for now more difficult for me, but i am continuing to try to imagine : could i come up with solution this by myself ? 

You have used first the formulae for the 1/2  of a circle segment as i have seen here. ( how do you get this ..from a handbook?) 

http://www.pandd.demon.nl/numwis/cirkelsect.htm#een

 
Has Maple a inbuilt formulae repository for handling euclidian geometry ? 

@Ronan 

Thanks

Did not account for it  radians or degrees in GX, but now i do. 
Removing the absolute stripes could be better , because Maple get be freed from this calculation

If the answer is - then make it +  ..or make this no sense ? 

There are more approaches for solving of course and using export in Geometric expressions gives this pic
But doing this with Maple..

Note : those absolute (modulus) |  is for a positieve area meant ?, so leaving them out is easier for Maple to handle the equation ?

@Ronan 

Thanks

You do it better then my, because my equation seems to still be correct but another one unsolvable.

The question was about two farmers : http://www.davdata.nl/math/grazinggoat.html

R = 1.1587 L  ( L is radius smallest circle ) 
If R has this length : half of smallest circle can be grazed.
  

Geometric expression can perhaps figure out the solution for the overlapping circles , but i did not yet figure out how to to this.