BLOG ENTRY #5

SINCE MY LAST BLOG ENTRY I HAVE BEEN INVESTING THE QUESTION: HOW IS THE DIOPHANTS FORMULA RELATED TO THE PYTHAGOREAN THEOREM FORMULA IF THERE ARE ANY RELATIONS AMONG THE TWO AT ALL?
I DID THE SAME THING FOR A DIFFERENT SET OF TRIPLES THAT I DID FOR THE TRIPLE 3-4-5 IN THE PREVIOUS BLOG ENTRY. THE TRIPLES THAT I USED SECOND WAS 16-20-12. WELL I STILL DONT KNO HOW TO GO ABOUT WORKING THE DIOPHANTUS FORMULA BACKWARDS SO I STUCK WITH REARRANGING THE PROCESS. I KEPT THE 1ST STEP:

• 2*4*(2)= 16

THEN INSTEAD I DID STEP 3 SECOND:

• 4^2-2^2= 16-4= 12

THIS WAY I HAD SIDE LENGTHS "a" AND "b">>SIDE LENGTH "a"= 12 AND SIDE LENGTH "b"= 16
I STILL SEEN THE PATTERN THAT I CAN GET THE HYPOTENUSE 2 DIFFERENT WAYS. I COULD DO STEP 2 OF THE DIOPHANTUS FORMULA:

• 2^2+4^2= 4+16= 20

{IF I WAS TO DO THE SECOND PART LAST I REALLY COULD HAVE JUST DONE ALL THE STEPS IN ORDER BECAUSE EITHER WAY I WAS USING THE FORMULA BUT LOOKING AT THE FORMULA IN A DIFFERENT WAY WAS AS USEFUL TO ME AS DOING IT IN THE ORDER DIOPHANTUS WAS QUOTED ON IN MY 1ST BLOG ENTRY.}

OR I COULD HAVE USED THE FORMULA FOR THE PYTHAGOREAN TRIPLE:

• a^2+b^2= c^2

• 12^2+16^2= 20^2

• 144+512= 400

• 656≠ 400

SO IN CONCLUSION MY THEORY OF THE PYTHAGOREAN THEOREM AND THE DIOPHANTUS FORMULA HAVING SOME KIND OF RELATIONSHIP WITH EACH OTHER IS ABSOLUTELY NOT TRUE. IT IS NOT TRUE BECAUSE IT DOESN'T WORK FOR EVERY TRIPLE. THIS MEANS THAT IT ONLY WORKED FOR THE TRIPLE, 3-4-5 BECAUSE IT WAS A COINCIDENCE. THEN AGAIN I ONLY EXPERIMENTED WITH TWO TRIPLES WHICH WERE: 3-4-5 AND 12-16-20 SO IT COULD HAVE ONLY DIDN'T WORK FOR THE 12-16-20 TRIPLE OR IT COULD HAVE ONLY WORKED FOR THE 3-4-5 TRIPLE.

WHAT IS THE REASON THE PYTHAGOREAN THEOREM AND THE DIOPHANTUS FORMULA DON'T MIX OR CANT WORK TOGETHER TO GET TRIPLES? WHAT IS THE MAIN PROBLEM OR GLITCH THAT WONT ALLOW THIS TO WORK? IS THERE ANY WAY TO MAKE IT WORK? FOR EXAMPLE CAN YOU GO AROUND THE PROBLEM AND MAKE A SOLUTION TO IT?