@Rouben Rostamian  

So welcome and thanks a lot 

To important cases you mentioned

@Alsu I follow your works

@Markiyan Hirnyk thank you

Maplesoft Developers are Not only the most gifted Mathematician Team who devoted their efforts for assisting thousands Researchers Minds but also their Spiritual development .
Unlike ! Wolfram that prefered trade and advertising over solving main problems ...

Maple Version Release Dates 1980—2009

    Maple 13:Apr 2009
    Maple 12: May 2008
    Maple 11: Mar 2007
    Maple 10: May 2005
    Maple 9.5: Apr 2004
    Maple 9: Jun 2003
    Maple 8: May 2002
    Maple 7: Jun 2001
    Maple 6: Feb 2000
    Maple V Release 5: Jan 1998
    Maple V Release 4: Jan 1996
    Maple V Release 3: Mar 1994
    Maple V Release 2: Nov 1992
    Maple V: Aug 1990
    Maple 4.3: Mar 1989
    Maple 4.2: Dec 1987
    Maple 4.1: May 1987
    Maple 4.0: Apr 1986
    Maple 3.3: Mar 1985
    Maple 3.2: Apr 1984
    Maple 3.1: Oct 1983
    Maple 3.0: May 1983
    Maple 2.2: Dec 1982
    Maple 2.15: Aug 1982
    Maple 2.1: Jun 1982
    Maple 2.0: May 1982
    Maple 1.0: Jan 1982
    The initial research-project software was named Maple in Dec 1980

@Markiyan Hirnyk 

thanks a lot for remarkable reference
best wishes by Fereydoon Shekofte

@Kitonum 

Yes master i understand the trick of two polygon with epsilon distance

But it cause double work for hardware to deal with them !

I am not familiar with directx or opengl programming a lot !

But i remember there are options for back face culling ... Or similar tasks that will done by Gpu itself !

Are you sure today Gpus nvidia or intel .. Doesn't support automatic coloring of both faces !!!

Markiyan Hirnyk

If there were many fans like you for providing mathematical proofs through Maple ! then in the near future our computer algebra system not only could solve problems symbolicaly even can be a great assistant for helping to underestand proofs more easier

anyone know ? whether both face rendering of polygons are built in the modern GPU ?

Problem  Solved  by Chinese Mathematicians ?
but i could not find any comprehensive materials on web how they expained the solution ?
how they did use power of computer for finding proofs ?
 

thanks a lot Kitonum

it must be very useful for research on pixel based shapes

dear Alsu did you stop posting topics ?

I am proud to Hail Erik Postma

Kitonum thanks a lot

   I admire all  the Maple developers and their team work spirit !

To be a mathematician demand the creed of Pythagoras ... Einstein that made millennium. names for humanity !

Unlike the Stefan wolfram that prefered marketing rather than the Creed of a real Mathematician !

he assuming himself as a prophet like Moses and wrote huge book as Tora and all the rest of mankid must obey the only ten commandments he manage ...