Derivation of additional formulae for Pythagoras Theorem
I was 16 years of age, when I had just finished my Form 6 exams (HSC), during the holidays I invented an alternative set of formulae for Pythagoras Theorem. I did not know how to get my paper published so my dad, Dr. M. Balasundram, the Radiologist at Seremban General Hospital wrote to several universities to have my paper published.
Attempted to publish formulae for Pythagoras Theorem
I remember that the two Chinese professors at University of Malays had written back to ask me to have my paper translated into Malay. I am searching for that letter and when I find it I will publish it in this article. I do not know why they had asked me to translate the paper into Malay language as our medium of education was in English, those days, so I had very little knowledge of Malay and I could not translate the paper. Finally, looking back at events 44 years ago I believe they did not want me to publish the paper.
I could not prove Fermat's Last Theorem and my dad misundertood or mistyped the letter above - a third party was typing out the letters as we did not know how to type. I corrected it but I have not found the copy of the original letter sent to Cambridge University. That is why this draft version is shown. When I do find the copy of the letter sent to Cambridge University, I will reproduce it here in this article.
After years of silence and abuse by powerful people I have decided to speak out. From published newspaper articles and personnel experience, I want all my readers to know that the Malaysian government denys scholarships for non-Muslim students to study at Cambridge or Oxford Universities. Only Muslims are allowed to study at those universities. It is an unwritten law among the Muslims.
This is the reason I am publishing this paper on my blog. The letters below from University Malaya was sent to me much later.
Fermat Last Theorem
How did I arrive at these formulae for Pythagoras Theorem? Actually I was trying to solve Fermat's Last Theorem. As I played around with the numbers and looked at how numbers behaved I discoverd the formulae for Pythagoras Theorem.
I quote wikipedia
"In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation
xn + yn = zn
for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known to have infinitely many solutions since antiquity"
Formulae for Pythagoras Theorem
I have take photographs of the original letter sent to University Malaya and have shown them here below.
The formulae for Pythagoras Theorem
[(2a-c)c]2 + [2a(a-c)]2 = [2a(a-c)+c2]2
which is represents the terms
X2 + Y2 = Z2
a and c can have any interger value and when c is divisible by 2 the formula is reduced to :-
[(2a-c)(c/2)]2 + [a(a-c)]2 = [a(a-c)+(c2/2)]2
- Dr. Peter Achutha, 30th July 2018