Mathematical Discoveries ### Introduction to Regenerative Mathematics

November, 2013

The mathematical brainchild "Kola Analysis otherwise known as Regenerative Mathematics" came to me in 1993 as a fantasy of my head in form of impulses of thought saying, "You can formulate formulas", when I was meditating on Newton's First Law of Motion which states that, " Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change state by forces impressed on it." Four years later, I found myself in this new mathematical world faced with the challenges to unravel the hidden knowledge embedded in it. Today is no more a fantasy but a reality that has given birth to a new line of thoughts and many fingers of vision and dream.

Philosophical Backgrounds of Regenerative Mathematics

Regenerative mathematics, a mathematical regeneration analysis, is all about regenerating the present state of a system, comprising a given number of grouped elements or objects which are grouped into two or more columns and rows in simple or multiple dimension, by using a totally controlled mechanism such as Logico- Sequential Distribution phenomenon to unravel the driving forces behind the cascade of events of the past that led to the emergence of the present state of the system so as to have full understanding of the past, the present and the future of the system under controlled mechanisms.

This mechanism should take on a degree of order, be totally controlled and characterized by features such as restraint, reciprocity, predictability, consistency and persistence. Henry C et al. (1968) wrote what Einstein called "the rabble of senses" that man must create for himself, some sort of world in which he can act effectively, a world which will take on a degree of order or system or meaning. This is the only kind of world in which man can act effectively. The knowledge gotten from this mathematical regeneration analysis will enable us to effect modification and reconstruction along the lines of improved productivity and efficiency in matters relating to the future significance of the system.

Fundamentals of Regenerative Mathematics

Regenerative mathematics is the mathematical analysis of a logical-mathematical intelligence phenomenon called Distributive Regeneration of Ordered System. Distributive Regeneration of Ordered System is a phenomenon which occurs when a given system of order comprising a number of elements (objects) that are grouped into two or more columns and rows is subjected to a Logico-Sequential Distribution for the purpose of regeneration. In addition, Logico-Sequential Distribution is a distributive phenomenon designed to make a given grouped number of elements in an ordered system to undergo a logical and sequential series of transposition until all the elements return to their original arrangement before being distributed.

Regenerative Mathematics Topics

• Analysis of Distributive Regeneration of Ordered System
• Positiomatics
• Complexity Emergence in Distributive Regeneration of Ordered System
• Cryptography and application of Distributive regeneration of Ordered System

### REGENERATIVE MATHEMATICS

Distributive Regeneration of Ordered System is a phenomenon which occurs when a given system of order comprising a number of elements that are grouped into two or more groups is subjected to a Logico-Sequential Distribution for the purpose of regeneration. Regenerative mathematics otherwise known as Kola Analysis is the mathematical study of distributive regeneration of ordered system. The concept of regenerative mathematics came into emergence when it was observed that a set of objects that were grouped into two or more columns and rows when subjected to Logico-sequential distribution returned to their original arrangement before being distributed after certain distribution number.

### SIMPLE DIMENSION POSITIOMATICS

Positiomatics was derived from the words "Position and Mathematics". Like regenerative mathematics of distribution of ordered system, Positiomatics is the mathematics of position changing, correlation and location of elements (objects) in an ordered system when subjected to distributive regeneration phenomenon using Logico-Sequential Distribution.

### DIMURELO PUZZLES

DIMURELO is a logical-mathematical intelligence puzzle developed from the aspect of Kola Analysis named Complexity Emergence in Distributive Regeneration of Ordered System. Unlike Sudoku which is a (sometimes addictive) puzzle, Dimurelo is basically a distributive puzzle presented on a square or rectangular grid in a distribution form. The puzzle revolves around the four core characteristics of logical-mathematical intelligence. They are concrete reasoning which involves breaking down systems into their components; linear reasoning which involves seeking order and consistency in the world; causal relationships which involve identifying cause and effect within a system; abstract reasoning which involves using symbols that represent concrete ideas, and lastly complex operations which involve performing sophisticated algorithms.

### CARD MATHEMATICAL INTELLIGENCE GAMES

If magic is the use of intelligence in form of tricks, deception or strategies to produce mysterious, amazing and mind-blowing results then card mathematical magic can be defined as the use of mathematical intelligence in form of card tricks or strategies to produce mysterious, amazing and mind-blowing results. The novelty of card mathematical intelligence game tricks is that they are based on simple mathematical principles. The principles underlying card mathematical intelligence game tricks were coined out from distributive regeneration of ordered system (Taylor, 2013).

### LOGICAL REASONING PUZZLES FOR CHILDREN

In school, pupils are taught how to do addition, subtraction, division, multiplication, and how to apply rules and formulas to solve problems but the creativity and intelligences that brought about all these mathematical operations are often neglected.For instance, logical-mathematical intelligence is the ability to reason, calculate, recognize patterns and handle logical thinking. It is usually found in researchers, scientists, computer programmers, engineers, mathematicians, doctors, police investigators, accountants, economists, lawyers and animal trackers. Famous examples well-known for logical-mathematical intelligence include: Sir Isaac Newton, Albert Einstein, Bertrand Russell, Marian Diamond, and Bill Gates.

### Problem I

Show that the regenerative distribution number of a given number of cards which are grouped into 5 columns with each column having 48,828,125 cards is 24.

### Problem II

In a football match opening ceremony, 120 students are needed to make a parade to grace the occasion. They are grouped into 12 columns with each column having 10 students and if their parade mechanism obeys Distributive Regeneration of Ordered System, calculate the Regenerative Distribution Number (t) of the arrangement.

### Problem III

If a student grouped 399 cards into 19 columns with each column having 21 cards, calculate (i) the last transposed version distribution number of the starting distribution (ii) if the numbers of columns and rows were interchanged what would be the new regenerative distribution number for this new arrangement. n (E) = 399.

### Problem IV

A mathematics tutor wanted to illustrate a card mathematical magic trick to his students. He gathered 100 cards into a deck with all the cards' faces down. He then asked four students to pick one card each without making him see the faces of their cards. After that, he divided 76 cards out of the remaining 96 cards into 10 columns and 8 rows. That is to say 6 of the 10 columns have 8 cards each and the remaining 4 of the columns have 7 cards each. He instructed the four students to put their chosen cards one by one on each of the 4 columns having 7 cards to make 8 cards. After that he distributed the rest of the cards on the columns to make 10 cards per column. If he subjected the cards to Logico-Sequential Distribution, at what distribution would all the cards' vertical position ranking values would be equal to the values of their horizontal position ranking values at the starting arrangement?

### Problem V

In a national festival to commemorate 100 years anniversary, a number of school pupils were needed to perform a choreography to grace the occasion. If the number of pupils needed was 100 and the organizers of the choreography thought it right to apply the principles of Distributive Regeneration of Ordered System for the choreographic mechanism. In order to conserve time, two mathematicians were given the challenge to determine and design the arrangement that would allow the pupils to return to their starting arrangement quickly.
The first mathematician came out with this arrangement: Number of columns (C) = 10, Number of pupils in each column= 10, & n(E) = 100
The second mathematician came out with this arrangement: Number of columns (C) = 5, Number of pupils in each column= 20, & n(E) = 100
(i) Which of these two designs would be more time saving?
(ii) If a pupil was in the horizontal position ranking value 35th at the starting arrangement (d0) in the arrangement fashioned out by the second mathematician, what would be her vertical position ranking value (Pvd0) at that starting arrangement?

### References

1. Taylor, Adekola A. (2016). Derivation of formulas for position change of entities in power inductive distribution. International Journal of Scientific and Research Publications 6(7):409-420.

2. Taylor, Adekola A. (2015). Quadratic distribution patterns in Kola analysis. Mathematical Theory and Modeling 5: 60-66.

3. Taylor, Adekola A. (2015). Derivation of formulas for position change in Kola analysis. International Journal of Scientific and Research Publications 5(11):101-109.

4. Taylor, Adekola A. (2014). Logical-mathematical intelligence for teens. Mathsthoughtbook.com

5. Taylor, Adekola A. (2013). Regenerative mathematics and dimurelo puzzles for children 8-12yrs. USA: Lulu Press Inc.

6. Taylor, Adekola (2013). Card magic and my mathematical discoveries. USA:Lulu Publishing.

7. Taylor, Adekola A. (2010). Kola Analysis: An inventive approach to logical-mathematical intelligence for secondary and advanced levels. Journal of Mathematical Sciences Education 1(1): 44-53.<