Swannies Theorems, Art in Maths and a follow-up to Pythagoras, De Tinseau and De Gua De Malves.

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   ^^^ INDEX^^^                                        SWANNIES ART / SWANNIES THEOREMS
                                       
all about *THE TRIRECTANGULAR TETRAHEDRON *
                                  
PYTHAGORAS  >  DE GUA  >  TINSEAU  >  PLATO > SWANNIE

                                 PYTHAGORAS'S  'Areas'  THEOREM (5C BC)  -   25 Centuries later  -  SWANNIES  'Volumes'   THEOREM (2006 AC)

2006:  First Theorem: Pages 1 - 5      2011 & 2013: Theorems II to X: Pages 8 - 10 Art: Pages 6-7 & 11-12
2012:  Squaring the circle: Page 13,   Ball Story: Pages 14-16:      2013: Golden & Platinum Ratios & Fairy: Pages 17- 21     
           SS
It takes about 80 minutes to read this.

I Therefore suggest that you page through first  (or start with the Art page if you are not really interested in the Maths details).  The photographs and diagrams alone should give a good idea of what the theorems are about; being simply the areas or volumes of  three shapes that add up to  give a fourth, all arranged on the four faces of a *corner of a box*. Not related to the theorems, you are rewarded with 'Ball and Bra' on the common origen of  two usefull commodities. --- Then if you found any of the pictures or diagrams interesting you may wish to check the written stuff. Please comment!
(For a Quick Look at the two main definitions (Theorem I: See the second definition (in bold) given on page 'Definitions '.and Theorem VI: See page 'VI to X', the definition (in bold).
 
                                 Swannie from Port Elizabeth, SA  (E-mail: swannie@ladygrey.co.za)

2015:  Note: The models and diagrams are now displayed in a cell of the old jail in Lady Grey. Should you visit this scenic town enquire at the Hotel/ Mountain View Country Inn to see these and more models. If Francois/Swannie is not in town Dalene may be able to oblidge.    

Copyright Notice: The contents of this site is the property of Francois Swanepoel. It may be freely used provided a theorem used/mentioned is referred to; as a Swannies Theorem, First or Second etc.as applicable; and reference is made to this website (Swannies Theorems or http://swannie.webplus.net) whenever any of the contents is used.  
                                              

First Theorem: A follow-up to Pythagoras,  De Tinseau
and De Gua De Malves. A Spatial, 3D, Volume -type theorem
that allows the design and building of an infinite number of models.    
In addition to the wish that it will contribute towards making
Maths more interesting for students Swannie wishes to reveal
the therapeutic value to a senior citizen of a quest for finding
a solution to a maths puzzle.
Whereas a problem in a maths text book - a De Gua De Malves
type problem (but this was only pointed out to him
afterwards and he was also off computers for years) got him
going, a fourth power area squared thing put him off track
for at least four months. During this time many little boxes of
many shapes were built out of frustration  but that and the
theorem models building is another story.

        

Pythagoras + De Tinseau + De Gua De Malves + De Trick = Swannie
What got the theorem going: The trirectangular tetrahedron, as per example shown above, with
with faces  A,B,C seen from above and D (and the sky!) reflected in a mirror, and the three lines below! ***

  Area A2 +  Area B2 +  Area C2 = Area D2        (De Gua De Malves)
{(A2)^1/3}^3   + {(B2 )^1/3}^ 3  + {(C2 )^1/3}^3  = {(D2 )^1/3}^3  (De Trick)
  x3 +   y3  +    z3 =   w3   (Swannie)

*** Please note that in this article ^ denotes a power/index of the previous number or bracket eg. 5^2  =  5².     a² or A cubed is shown as a2 and A3.

Below: Non theorem shapes, just to give some colour to the page.
On the left: A dodecahedron 'cut out' from a cube such as the one it is mouted on. Easy and quick to find the volume of the cube. Not so with the dodecahedron unless you do a 'dunk it' measurement with a large measuring cylinder and water! Could one call this one's centrepiece a twisted prism or perhaps an antiprism?
 On the right is a creation with the Moons of Hippocratus of Chios. The sections have whole number ratios between them: 28:8:7:4. The moons get explained under Potpauri so please for now just see it as 'Art'.                                                                                            ^^^^^^^^^ Return to horizontal Index at top of the page !!!

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