Sisonke Sandile Models and ideas in mathematics I have spent time on mathematics and have developed a keen interest in developing ideas and models of my own, inspired by great men and women with more education tha n I . So then, the re ader is encoura ged to look at m y work with an open mind and lenient re ading. If I have erred, it is only because I am in a formative stage in my development and am sure to improve . Mathematics is my passion, so is scien ce and I ca n not resist indulging my cre ative mind like this. You will forgive me for tha t which I am ignorant of but please enjoy whatever seems interesting Thank You. This work is dedicated to Srinivasa Ramanujan who also taught himself. 1. The identities of k(x;nx) K, a cons tant representing 2 , is central to our understanding of the decimal identit ies known as semidecimal Iden tities(known as that because they use the symbols 0 to 5 .K(2) always appears as a function of (x+nx0), where x=5 and n(x0) the n identities of K.The r e are multiple identities. 1.1.1 Primary Identity: 1.1.2 This is derived from complex numbers, where +nx0 becomes ( _nx0) (The subt ractive inverse o f ( +nx0) and an imaginary number is multiplied w here the sign is found.This is also an identity but we will deal with it later.Let us discuss the primary identity, (x+nx0). x is a constant 5 and the +sign is replaced with j^2, an imag inary number, which is multiplied with n(x0) , another identity. 1.1.3 The number identity The number ident ity is found in the primary identity and consists of a variable n with its M icro identity(x0).(x0 takes on numbers ; (0,1,2,3,4,5) each number produces a number identity.The following are the number identities, written in rectangular form, alo ng with x and their subtractive inverses.Note tha t there is a _ for the identity which marks it as a subtractive inverse. 1.1.4 The number identities (micro identities ) 1.1.5 (+n0;+n1;+n2;+n3;+n4;n5 ) 1.1.6 Primary identities (x+_n0) + (x+_n1)+(x+_n2)+( x+_n3)+(x+_n4)+(x+ _n5) 1.1.7 Subtra ctiv e inverses (x - 5)+(x - 4)+(x - 3)+(x - 2)+(x - 1)+(x - 0) 1.1.8 Primary Identity with imag inary number (x+ ( j ^2 ) 5)+(x + ( j ^2) 4)+(x+ ( j ^2) 3) +(x+ ( j ^2) 2)+(x+ ( j ^2) 1)+(x+ ( j ^2) 0) 1.2The O riginal Decimal Identity The original decimal identity is the number 10, on which the decimal system is based. I have tried t o derive a more interesting wa y to express it.I have writte n an equation whose solution is purely the number 10.I have also made use of 2 and the indices of 2 to try and express it as well as I can. 1.2.1 The Four Quadrants Using four quadrants has been a great graphical aid in derivi ng the identity.In each quadrant there is expressed a factor or multiple of 10.This is my guide in deve loping my equation. 10|2^10 10^2 |2*(1024) In the first quadrant, there is a base of 2 with an exponent of 10.I use 2 because when 10 is divided by 2, the result is 5, which is the A ’ of ourprimary identity. 2 is raised to 10=1024 2 nd quadrant is just 10 itself, for in the 3 rd quadrant we have the logarithmic inverse of 2^10 , 10^2. In the 4 th quadrant , it is 2*(1024).In anotherma nner we can express this in terms of the 10s. W e have : 10;10^2 2(10*10^ 2)+2((2*10)+(2)^2) 2(10^3)+2((2*10))+2(2^2) B etter expressed algebraically as: K ( z^3)+ k(k*z)+k(k^k) =2000+(2(20))+(2(2^2)) =2048 whic h is the double o f 1024 L et us now get to work on the original decimal identity equation. M atrix - k+c t 1 k;1;1 t 2 k;1;1 t 3 k;1;2 t 4 k;1;4 Matrix - 1/k+c t 1 k;4;2 t 2 c;3;2 t 3 k;4;2 (k+c)+((k+k)+k^2+c/k^2(k^2+k^2+k)+c(c ^2+c^2) /2 L et k^2(k^2+k^2+k)/k =A0 Let c(c^2+c^2 - k)/2 =B0 A0+ ( B 0 ) ( ^1/3) +k /k+c The original decimal identity is in use primarily as a shorthand for base 10, also for illustrative purposes as it consistently returns a number 10, this is why it can be used as an algebraic substitute for th e number 10.(to the power of one , a lthough it can be raised to a higher index by those who wish.