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

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Fairy 3


The Maths Fairy had to be credited somehow without then relating or even  having the above true story available. So Swannie credited her with 'throwing away part of some unknown unit,  one cm of  cm^4 to get a useful cm^3 - which in away is what  practically happened!

The comment earlier mentioned is now much appreciated as it led Swannie to give thought to a simple, but subtle subject, aided by ingrained  views, before this story could be generated. He surely now also has a better understanding of how  it all came  about!    
                                  
By the way the above somehow turned up this nonsense rhyme:-

               Numbers divorced, or rather apart, from units,       Sometimes they tend to hide,
               being all on their own,                                             but never from those who like to play with them,
               must be very alone.                                                 like making them add and divide.

The noun and verb that follows are relevant (please, also check in your Dictionary and Thesaurus):

     Theorem: A Mathematical Statement established by means of a proof.
* * Manipulate: More positive wording: To use with skill. More negative wording: To use deviously to own advantage.  

Yes Swannie did manipulate Maths to find his theorem and he really likes to think it was with skill,  and yes it was to his own advantage, it surely boosted his ego, but as to whether the maths was  used deviously he won't admit.  Whether the theorem is perhaps seen as trivial and seems to be of no practical use other than making little models, may be so, but Swannie has no doubt that it is valid. He also better feel good about it as it is the only original (to his knowledge)  discovery he has ever  made! (except perhaps also his unique treatment of piles with cold water). Thus he immensely appreciates it if any one bothers to comment and/or suggests an improvement.  
   
***  Note: The three above in bold is, I would say, incorrect  because area^2, as was shown, is length^4 . As "James Stewart" used De Gua's  number with unit^4 theorem he  should have said: This is a fourth-dimensional, version of the Pythagorean Theorem, or did he anticipate something like Swannies contribution? Perhaps just meant: taking it to a next level?

2.   In Brief

What follows would seem to wipe away most of the above directed at the First Theorem and make the theorem real elementary and straight foreward. This approach obviously initially bypassed  Swannie; being simply an 'abreviated' definition of De  Gua,s theorem:
The sum of the squares of the numerical values (only!) of the squares of the areas of the right angle faces of a trirectangular tetrahedron add up to the square of the numerical value (only!) of the area of the base of the tetrahedron.    
???   
Any problem with simply ignoring the units (?) So say a face has an area of  2,645...^2cm^2 , that is 7cm^2, ignore the unit and square the 7 only, that is 49 = 7 x 7   --- use the one 7 for the base of a prism on the face and now give it a cm^2 unit l, that is a base area of 7cm^2 --- then use the other 7 for the height  of the prism and give it a cm unit, that is a height of 7cm. So you have a volume  7^2 cm^3  for the prism = 49cm^3.
Thus are the units initially ignored as defined above  and lastly attached as required.
No Maths Fairy, no disappearance of units. How dull!  
  
 Below left: Crucifiction as still annually practised at Lady Grey. The torture is by near death freezing over a couple of hours in the cold dry high altitude air. Note: a Cross to be balanced and carried on the shoulder seems need to be of a three in one design (as are the theorems), the cross member halves and the vertical section above it adding up in length to that of the lower section of the post. It would require a real powerfull chap to carry the likes of the one used here.  Below right: Work of art never put to use except for taking hikers for a view of the gorge on the here shown side. The , the bridge to complement the tunnel to get a train across the gorge was never built.                    THE END (for now)

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