I thought Rouben's advice was very sound.  However, if you do go for an online course, be aware of scams.  I came across a drop-dead gorgeous Ukrainian/Russian woman giving a lesson on the gamma function on a U-tube video.  I also came across a complaint that she'd taken some guys money - and no satisfactory lessons! 

Thanks a million Acer!  I almost went insane trying to get the values.  I somehow thought fsolve, float, would give floating point values. It's very frustrating to see the correct values on the screen, yet not being able to use them!  I tried all sorts - like using the substring command to delete the first characters " x = " .  This "worked" in that the screen displayed the correct values - but I was still unable to use them in further calculations.   At least when you get an error message in Maple you have somewhere to start.

     Regards the Miquel 5 circle theorem,  I haven't had any replies from anyone whose heard of it.    I used to enjoy geometry problems as a young teenager.  I'm rather annoyed about my maths education, as on attending university I had to come to grips with Weierstrass''s 'epsilon delta method'!  It was as if I'd been put in a time machine and mathematical processes had changed radically! I think the reason is due to the rift between Newton and Leibniz for the discovery of calculus, as it caused a communication breakdown between European and British mathematicians for over 100 years.  Then, around 1900, Britain - after basking in Newton's achievements - found they were well behind in mathematical ideas of European mathematicians.  Their methods weren't as rigorous - so a catchup was needed!   

    Thanks for reading this far.  It is for general consumption - probably some other section of Male?. I'd be particularly interested in comments from people not brought up in Western  mathematics.

Thanks again,

  David

@Kitonum 

Thanks for that - my maths was OK - I forgot to put the sqrt in front of the 1/2 in the maple reply. :-(

Cheers,  David 

Hi Kitonum.  I modified the values.  I set ht:=sqrt(2/3):   hs:1/2: and st:=1:  

If my calculations are correct this ensures the faces of the tetrahedron and pyramid are equilateral triangles of side length one.  This was necessary for the puzzle - the answer is not 7!

Thanks again.

   David

Thanks Rouben for the program.

   David

Thanks  for that.  It worked better than I thought it would as I'm not familiar with much of the  program.  The only thing it balked at was the plot options view.  In the Maple 7 help section it has

  view=[xmin..xmax,, ymin..ymax ] for the curve displayed on screen.  The geom3d package has a view option as well.  

  The triangular faces of the tetrahedron and pyramid need to be congruent equilateral triangles, but I think I'll be able to suss out the maths for that.

Thanks again for your help.

Thanks Rouben & Kitonum for your help.  Regards Maple 7 I don't think it supports the style option in 2d plots. There is mention of Worksheet plot interface surfacestyle in the help section.  Also on the completed plot one can right click and select surface styles - Patch, Patch without gridlines,...,Point but I don't think they are programmable.

     There remains the mystery of the small black square being output in my original program, when I specified color=white.  Selecting various values for R gives different outputs - as expected - but some give error: 'non numeric vertex definition'.   I suspect this is due to a negative number in the sqrt().   What puzzles me is  the strange range of values of R.  R=12 works, then it balks at R=25, 29 & 30 are OK but not 31 to 33, 34-37 is OK, but not 38-40.

    ..but there are far more other mysteries in life to ponder😀

Thanks for all your help.

    David    

Thanks to Tomleslie for an easy way of my "hard way" method.  I wish to describe why I persued the "hard way", and in the process it poses more questions about Maple - and some unanswered questions I originally asked.

  I wanted to draw a circle colored green so I entered:

C1:=circle ([0,0],r,color=green):

       This produces a circle as if it had been drawn with a green crayon and compass.  ...but I wanted the interior to be filled!  ...so I next entered: 

C1:=circle ([0,0],r, filled=true, color=green):

  This did not give the required result - but neither did it give an error message!  Searching on the help menu, there is nothing mentioned for 'filled'.  That is why I resorted to the hard method.  To my mind, a disk is a three dimensional entity, like a CD.  A circle is 2D.  I looked 'disk' in the dictionary and found that in North America, the words disk and circle are much the same: eg "the moon''s disk hung in a cloudless sky".

   So I was duped by the American language😁  Questions posed are why did Maple 7 not flag an error message for filled=true? 

  In the rectangle command, what if one just wants to draw the perimeter of a rectangle?  Wen the color option is used the recangle is automatically filled with colour.

    And in my original post I drew a square comprising of a sequence of concentric rectangle commands, specifying color=white.  Despite this, it draws a sequel of black squares!  I have since experimented with the programme and it is sensitive to values of R (the radius of the circle, making the square of side 2R.)  Try values of R = 49, 55 & 60 for differing results.  One returns an error message.

  Again, thanks, and any answers to my questions would me most appreciated.

David

Thanks for your prompt replies.  I managed to get the animation to work.  In a similar fashion to the triangle I defined Circ as the circumcircle of the triangle, and added noslides:=16:

display(seq{Circ||i$50, t1||i$50}, i=4..noslides), insequence=true, scaling=constrained);

The circumcircle goes through all three points of the triangle, but in mine there appeared a slight difference in the top vertex of the triangle.  I'm not sure if that is an optical illusion, a bug in the software or my eyesight!

    I'm interested in constructing an acute angled triangle (ie all three angles are less than 90 degrees) given the three altitudes.   The problem of drawing a triangle given the three sides is relatively easy.  Ignoring translations, & rotations the triangle is unique.  Given the three altitude lengtths, is there a unique triangle that can be drawn?  Is there a command in thee geometry package that solves this with only a few keystrokes? Apparently there is nothing in Euclids Elements about altitudes, and I was surprised to see a few geometry theorems stated & proved  in recent times.

  I will peruse your solutions in more depth tomorrow.  Thanks again; goodnight andHappy New Year.  

Thanks heaps for that Kitonum.  That clears things up a lot for me.  I'm quite intrigued with altitudes. The three altitudes are concurrent at the ortho centre - something not mentioned in Euclid Elements.  To draw the altitudes of a triangle, given its three sides is easy.  To draw a triangle given the three altitudes is a little harder.  The case of a right angled triangle is simple enough, but to construct any other is harder.  I'm not even sure if there is a unique triangle.  That's my next task!  I found the info from the Wolfram maths site informative regards altitudes.  It has a few formulae there I might play with.

    I found the Maple help on 'intersection' rather distracting.  It mentioned it in terms of sets -and for some reason I thought it wasn't related to the geometry package😣

  Thanks again & a Happy New Year.

    David

Thanks for that.  It now works in Maple 7.  David

Thanks for your interesting answer.  However I forgot to mention I'm using Maple version 7, and I don't think the following commands are understood.

convert(evalf[4](solvec), list);  # Convert to the list and remove extra zeros
sol:=rhs~(%);  # Extract numeric values

David

@tomleslie   Thanks for that.  I was considering purchasing a book by th publisher O'Reilly, but it is far too advanced for me.  I'll stick with the search engine.  David

@tomleslie   Wow!  You've opened up a new powerful  topic for me which will be very useful.  I have been playing with the solution of a 5 by 5 crossword puzzle where there are 5 across words of 5 letters and also 5 intersecting 5-letter words.  I'd got lists of the possible ten words, but was using simple if statements to try and determine the possible words.  There's a book reference mentioned in the Maple Help section: 'Mastering Regular Expressions' by Jeffrey E F Friedl,   1997 which I must investigate.  

  Thanks again for your immense help. Must get some "shut eye" - it's almost 3am local time here!

David 

@Kitonum Thanks for that - a great help.  David