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 -
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:-
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-
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 -
Thus are the units initially ignored as defined above and lastly attached as required.
No Maths Fairy, no disappearance of units. How dull!