LOGO-L> what is the wrong with trigonometry

[MHELHEFNY@FRCU.EUN.EG]

Andrzej Baczynski wrote :-

>Hello Turtles,
>I have found an old mail (dated October 23) from Mr. MHELHEFNY, with 4 methods
to
>draw a sphere in MSWLogo 3D. There are Christmas coming, and I found that one 
>more way to produce a sphere (i.e. a bulb for a Christmas Tree) may be useful. 
>This is a short and simple, I hope, procedure. It use only rudimentary turtle 
>move commands and applies very little trigonometry. (I'm proud of this).  
>It should be run in PERSPECTIVE mode, of course. 

>This is a procedure itself:

to sph4 :z :w :dx 
 localmake "om (180 / :z / :w)
 localmake "fi arctan (1 / :z / 2 )
 repeat (:z * :w) [up :fi fd :dx*sin (repcount * :om ) down :fi rt (360 / :w) ]
end

>There are 3 questions, which a demanding student may ask:
>1-	Is it really a sphere ?
>2-	Where is a centre?
>3-	How to draw only a visible hemisphere?
>I have no students, so I don't need to look for the answer.
_________________

;For the second time hi Andrzej !
;George Mills told you to look for the code of the sphere in the solar
;example of MSWLogo.
;Here is the code reworked from that example to draw a real sphere of
;radius :r with even less use of trigonometry since a sine was used
;once only;besides we know where its centre is :-

to sph1 :r :step
 make "n 180/ :step
 repeat :turns[make "g repcount* :step-90 make "k :r* sin :g 
 make "rad sqrt(:r* :r- :k* :k) fd :k down 90 circle :rad up 90 bk :k]
end

This is not an attempt to reduce the value of your clever code; but
we should try to make the code clear for our students.

Now Yehuda will critisize my code for these 3 makes let me in advance
say what is the wrong with make ? what is the wrong with trigonometry ?
Merry Christmas !
Best Regards !
Mhelhefny
;----------------
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