@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. 
 

@Ronan 

Hello,

It is a Curvilinear Polygon

You draw the two circles and add the two intersections points ( via contstruct panel: intersection) and these two points are used for the definition of the overlapping area of the two circles.

Choose the arc- drawing  in the drawing panel , then click on a intersection point and drag a curvelinear line to the other intersection point.

Now this a half part and back again for the other part.

Then select the area and then calculate symbolic area ( see panels ).

@Rouben Rostamian  

Thanks

Clever done this by you and experienced user i think.

It started with a (big) circle c1 with his midpoint in the center of a xoy  coordinate system.
c2 is a circle with his midpoint on x-axis ( R, 0 )

We can calculate half of the blue area with two integrals for the upperparts of the two circles
For circle c1 there can be a area integrated from X (intersection ) to X= L along the x-axis. 

For circle c2 there can be a area intergrated from XOZ (x=0) to X (intersection )  along the x-axis
 

This two values of the integrated areas, doubled gives the blue area  sketched in Geometric Expression. = A
We get a equation.

Note: never have seen this %[1] : if % can have multiple output ? ( depends on input : here on one line with mutiple input )

Only the integration with ( integration interval , ? , ? ).

That's it.

@Mariusz Iwaniuk 

Hi, this is the formulae and useless 
 

Download de_koe_in_het_weiland1.mw

@Rouben Rostamian  

Thanks

Found this in old studymaterial and there it can be solved on a standard way

http://www.davdata.nl/math/grazinggoat.html

 Or advanced with a double integral and polar coordinates , what you did i think.
Unfortanely i must overhaul my old studymaterial ( made in Maple V )  about the double integrals

@Mariusz Iwaniuk 

Thanks

I think it has to do that the formulae is not correct, that i did not defined it correct in Geometry Expression.
Must look again to it. 

Looking a the midpoints of triangle and inscribed ellips can be also studied with Geometry Expressions

Geometry Expressions is the world's first application that lets you visualize geometry and formulate symbolic expressions by constructing a sketch. 
Simply sketch your geometry, add symbolic constraints, and then automatically output symbolic measurements and expressions. 

Its only 10 USD for program now..a bargain.

Results found in GE can be copied and pasted into Maple for further simplification 
A solid knowledge of the old Greek geometry is needed as base.. 

Note: a good example for me to see , because i do see some programing constructs in it what i encountered  here on the forum asking about programming.

You can go further with advanced mathematics for exploring this ellips 
Is it possible to get the code behind this worksheet ?

314301_mardentheorem.mw

@tomleslie 

Thanks!

For the extensive answer.

Was it in the Riemann sum example that a function what is passed to the procedure was already defined as a function with a arrow operator.

X:= Array(0..N, [seq(j, j=a..b, (b-a)/N)]): # x values stored in array 
 Y:= Array(0..N, f ~ (X)):   # y -values stored in array
 

Now in this example of Polygonal approximation the function is defined as a expression , so this must first defined as a function in order to use the ~ elementwise operator.

xv := Array ()  # x- values stored in array 
yv:=unapply( f, indets(f, 'name')[]) ~ (xv);   y-values stored in a list ?  ..no as a array as showed the ouput 

I noticed the difference between '[ ]' and [ ] 

Think i understood it now for the f part 
In the book the functions are given as expressions. 

return display ( ) .. to make sure there will be a plot ?

I try the attached functions in the book example...but noticed the procedure definition by p,L := approxL ( ):

Why is that ?

@tomleslie 
Thanks

First there is a series x-values stored in Array xv 

Its a difficult one to decipher. yv:=unapply( f, indets(f, 'name')[])~(xv);  What is the idea behind this statement    

yv := xv^3 - xv*sin(xv)  outside the procedure call 
unapply( ) should make a function from the expression in  ( ) 

Problem to check the outcome from statements in procedure , beause it are local variables ?

Complicated this.