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### Mathematics

 The category of mathematics are works on the abstract study of subjects encompassing quantity, structure, space, change, and more; it has no generally accepted definition.

### O Na Mole E Ke Anahonua (About the Roots of Geometry)

##### By: A. M. Legendre

1. O ke Anahonua ka mea e i ike ai ke ano o na mea i hoopalahaiahaia, oia na kaha, a me na ili, a me na paa. Ekolu mau ano o na mea i hoopalahaiahaia, he loa, he laula, a he manoanoa. 2. O ke kaha ; he loa wale no ko ke kaha; aole laula, aole manoanoa. O na welau o ke kaha he mau kiko ia: nolaila, o ke kiko, aole ona loa, aole laula, aole manoanoa, aka he wahi e ku wale ai no. 3. O ke kaha pololei ka loa pokole mai kekahi kiko a i kekahi kiko. 4. O ke kaha pololei o...

### Na Haawina Mua O Ka Hoailona Helu (First Lessons in Algebra)

##### By: Lahainaluna

Kuai kekahi keiki i ka ohia a me ka alani i na keneta he 12, no ia mau mea. Ua oi pakolu hoi na keneta o ka alani imua o ko ka ohia. Ehia na keneta o kela a o keia? E kau iho i ka w i hoailona no na keneta o ka ohia. A o ka w ke kumukuai i ka ohia, a he pakolu ko ka alani i ko ka ohia; nolaila, he mau w ekolu ke kumukuai i ka alani. He w hookahi ko ka ohia, a he akolu mau w ko ka alani, ina e huia lakou, he mau w eha o ka huina. Aka, he 12 na keneta i lilo no ia m...

Ua oi pa 4 aku na makahiki o Ioane imua o ko Iakobo; a o ka huina o ko laua mau. makahiki, he 20 ia. Ehia na makahiki o kela, o keia? E hoailona i na makahiki o Iakobo i ka w, no ka mea, he pa 4 na makahiki o Ioane i ko Iakobo, 4 mau w ka hoailona o kona mau makahiki. Nolaila, hookahi w a me 4 w, oia no 5 w ka huina o ko laua mau makahiki. Aka, he 20 ka huina o ko laua mau makahiki; nolaila, ua like 5 w me ka 20, a o ka w hookahi me ka hapa 5 o ka 20, oia na makahik...

### He Huinahelu (A Combined Arithmetic)

##### By: George Leonard

This volume contains basic mathematics (in Hawaiian). It teaches you the numbers in Hawaiian up to one hundred and also basio useful mathematics.

Ehia kahi iloko o ka 10? He 10 a me na kahi ehia iloko o ka 12? He 10 a me na kahi ehia iloko o ka 13? 14? 16? 19? 15? 18? 17? 11? Ehia na umi iloko o ka 20? iloko o ke 30? 40? 60? 80? 60? 70? 50? 90? 100? Ehia na umi a me na kahi iloko o ka 21? iloko o ka 23? 28? 26? 32? 35? 37? 44? 49? 41? 53? 57? 62? 65? 68? 71? 76? 99? 85? 87? 88? 92? 94? 99? He umi a me 1, heaha ia? 10 me 3? 10 me 7? 10 me 9? 2 umi? 2 umi me 1? 2 umi me 5? 2 umi me 7? 3 umi? 3 umi me 2? 3 umi me ...

### He Helu Kamalii (A Child's Arithmetic)

##### By: Wiliama Fowle

This volume teaches you children's basic arithmetic in Hawaiian.

No ka hana ana i keia Helu, e ahu no ke kumu i mau hua poepoe he kanaha a keu paha i mea heluia; pela no kela keiki keia keiki e ahu no lakou i na hua like. A like me ka hana ana a ke kumu, pela hoi e hana?i kela keiki keia keiki i kana mau hua iho.

### Principa Mathematica

##### By: Isaac Newton

Philosophiæ Naturalis Principia Mathematica, Latin for "Mathematical Principles of Natural Philosophy", often referred to as simply the Principia, is a work in three books by Sir Isaac Newton, first published 5 July 1687. Newton also published two further editions, in 1713 and 1726. The Principia states Newton's laws of motion, forming the foundation of classical mechanics, also Newton's law of universal gravitation, and a derivation of Kepler's laws of planetary motion ...

### Gentle Introduction to Dependent Types with Idris

##### By: Boro Sitnikovski

Dependent types are a powerful concept that allows us to write proof-carrying code. Idris is a programming language that supports dependent types. We will learn about the mathematical foundations, and then write correct software and mathematically prove properties about it. This book aims to be accessible to novices that have no prior experience beyond high school mathematics. Thus, this book is designed to be self-contained. The first part of this book serves as an intr...

### The Distribution of Natural Numbers Divisible by 2, 3, 5, 11, 13 a...

##### By: Harry K. Hahn; Harry K. Hahn

The Square Root Spiral ( or “Spiral of Theodorus” or “Einstein-Spiral” ) is a very interesting geometrical structure, in which the square roots of all natural numbers have a defined (spatial ) position to each other. The Square Root Spiral develops from a right angled base triangle with the two legs ( cathets ) having the length 1, and with the long side ( hypotenuse ) having a length which is equal to the square root of 2. The Square Root Spiral is formed by further...

From the image FIG 1 it is evident that the numbers divisible by 2 ( marked in yellow ) lie on defined spiral graphs which have their starting point in or near the centre of the square root spiral. These spiral graphs have either a positive or a negative rotation direction. A spiral graph which has a clockwise rotation direction shall be called negative (N) and a spiral graph which has an counterclockwise rotation direction shall be called positive (P). The gre...

### The Ordered Distribution of Natural Numbers on the Square Root Spiral

##### By: Harry K. Hahn

The Square Root Spiral ( or “Wheel of Theodorus” or “Einstein Spiral” or “Root Snail” ) is a very interesting geometrical structure, in which the square roots of all natural numbers have a clear defined spatial orientation to each other. This enables the attentive viewer to find many interdependencies between natural numbers, by applying graphical analyses techniques. Therefore the square root spiral should be an important research object for all professionals working ...

Another striking property of the Square Root Spiral is the fact, that the square roots of all square numbers ( 4, 9, 16, 25, 36… ) lie on 3 highly symmetrical spiral graphs which divide the square root spiral into 3 equal areas. ( see FIG.1 : graphs Q1, Q2 and Q3 drawn in green color ).

### The Distribution of Prime Numbers on the Square Root Spiral

##### By: Harry K. Hahn

The Square Root Spiral ( or “Spiral of Theodorus” or “Einstein Spiral” ) is a very interesting geometrical structure in which the square roots of all natural numbers have a clear defined orientation to each other. This enables the attentive viewer to find many spatial interdependencies between natural numbers, by applying simple graphical analysis techniques. Therefore the Square Root Spiral should be an important research object for professionals, who work in the fiel...

Another striking property of the Square Root Spiral is the fact, that the square roots of all square numbers ( 4, 9, 16, 25, 36… ) lie on 3 highly symmetrical spiral graphs which divide the square root spiral into 3 equal areas. ( see FIG.1 : graphs Q1, Q2 and Q3 drawn in green color ).

### Boole's Algebra of Logic 1847 : an Annotated Version of "Mathemati...

##### By: Stanley N Burris

This annotated version of Boole's "Mathematical Analysis of Logic" makes the extent to which Boole based his algebra of logic on the algebra of the integers. Problems are pointed out that will be dealt with in his famous 1854 "Laws of Thought"

The algebra Boole used in MAL to analyze logical reasoning is quite elementary, at least until the general theory starts on p. 60. But there is much that needs to be clarified---on many a page one can ask "Exactly what did Boole mean to say here?"

### On a New Method of Multiplication and Shortcuts : Volume 2

##### By: Artem Cheprasov

A completely new and unique method of multiplication where you can: 1.) Multiply positive numbers, get negative answers, and still achieve the correct positive result. 2.) Attach numbers to one another to bypass multiplication and addition steps. 3.) Choose one of many different paths to solve the same problem based on your own individual strengths and preferences. 4.) Multiply numbers into the billions with ease!

### Sketch of a Doctoral Program in Classical Mathematics : With an Em...

##### By: Jonathan Jacob Kenigson

This work is a brief set of notes; it has warrant neither to a claim of comprehensiveness nor of context. It represents the beginning of an odyssey toward realization of the classical ideal in mathematics education at the doctoral level.

### El número áureo en relatividad

##### By: Pedro Hugo García Peláez

El número áureo en relatividad Un libro científico sobre la razón de oro y una base de polinomios que satisfacen ese número

Pero al intentarlo con las transformaciones de lorentz que explican matemáticamente la teoría de la relatividad de Einstein, ya me convencí absolutamente que había demasiadas casualidades entre la teoría de la relatividad y el número áureo si considerábamos la fracción la velocidad de un objeto respecto a la velocidad de la luz igual a 0.681 o sea el inverso del número áureo. Metiendo estas relaciones en ambas fórmulas y aplicando logaritmos encontré hasta diez medic...

### Development strategies for the postal sector: an economic perspective

##### By: Dr. José Anson; Joëlle Toledano Bialot

This book examines the economics of the postal sector through three lenses: snapshot and trends, models, and opportunities. In the years to come, the Universal Postal Union plans to develop its role as a knowledge centre for the postal sector from these perspectives. At this time of radical transformation of the postal sector, it is important to understand how the sector has evolved historically, how it is connected with the economic system, and where it is heading. T...

### Onko Tonko : Puzzles for the Math Mentalist

##### By: Surajit Basu

This is a collection of puzzles requiring in most cases – high school math. The purpose is not necessarily to solve these problems, but to get you to think about different types of math puzzles. Many of the puzzles are introductions to different areas of math. Most of these puzzles can be done mentally. If you have to write, expect to write no more than a page. Pictures are useful.

“There are three planes”, said Onko, “which take off simultaneously - from Bangalore, Athens, and New York.” “Each plane goes 500 km north, then 500 km east, then 500 km south, and then 500 km west.” “Which plane is closest to its starting point?”, said Onko with a smile.

### Wandering in the World of Smarandache Numbers

##### By: A.A.K. Majumdar

In writing this book, the first problem I faced is to choose the contents of the book. Today the Smarandache Notions is so vast and diversified that it is indeed difficult to choose the materials. Then, I fixed on five topics, namely, Some Smarandache Sequences, Smarandache Determinant Sequences, the Smarandache Function and its generalizations, the Pseudo Smarandache Function and its generalizations, and Smarandache Number Related Triangles. Most of the results appea...

### Vedic Mathematics : 'Vedic' or 'Mathematics' : A Fuzzy & Neutrosop...

##### By: Florentin Smarandache; W. B. Vasantha Kandasamy

This book has five chapters. In Chapter I, we give a brief description of the sixteen sutras invented by the Swamiji. Chapter II gives the text of select articles about Vedic Mathematics that appeared in the media. Chapter III recalls some basic notions of some Fuzzy and Neutrosophic models used in this book. This chapter also introduces a fuzzy model to study the problem when we have to handle the opinion of multiexperts. Chapter IV analyses the problem using these mode...

We then remove the common factor if any from each and we find x + 1 staring us in the face i.e. x + 1 is the HCF. Two things are to be noted importantly. (1) We see that often the subsutras are not used under the main sutra for which it is the subsutra or the corollary. This is the main deviation from the usual mathematical principles of theorem (sutra) and corollaries (subsutra). (2) It cannot be easily compromised that a single sutra (a Sanskrit word) can be mathemat...

### Unfolding the Labyrinth : Open Problems in Physics, Mathematics, A...

##### By: Florentin Smarandache

Progress and development in our knowledge of the structure, form and function of the Universe, in the true sense of the word, its beauty and power, and its timeless presence and mystery, before which even the greatest intellect is awed and humbled, can spring forth only from an unshackled mind combined with a willingness to imagine beyond the boundaries imposed by that ossified authority by which science inevitably becomes, as history teaches us, barren and decrepit. ...

After the experiments were completed, the life span of such “atoms” was calculated theoretically in Chapiro’s works [61,62,63]. His main idea was that nuclear forces, acting between nucleon and anti-nucleon, can keep them far away from each other, hindering their annihilation. For instance, a proton and anti-proton are located at the opposite side of the same orbit and move around the orbit’s centre. If the diameter of their orbit is much larger than the diameter of the ...

### Scientia Magna : An International Journal : Volume 3, No. 3, 2007

##### By: Shaanxi Xi'an

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics.

An identity involving the function ep(n) Abstract The main purpose of this paper is to study the relationship between the Riemann zeta-function and an in¯nite series involving the Smarandache function ep(n) by using the elementary method, and give an interesting identity. Keywords Riemann zeta-function, in¯nite series, identity. x1. Introduction and Results Let p be any fixed prime, n be any positive integer, ep(n) denotes the largest exponent of power p in n. Th...

### Scientia Magna : An International Journal : Volume 3, No. 4, 2007

##### By: Shaanxi Xi'an, Editor

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics.

A structure theorem of right C-rpp semigroups1 Abstract A new method of construction for right C-rpp semigroups is given by using a right cross product of a right regular band and a strong semilattice of left cancellative monoids. Keywords Right C-rpp semigroups, right cross products, right regular bands, left cancellative monoids. x1. Introduction Recall that a semigroup S is called an rpp semigroup if all its principal right ideals aS1, regarded as right S1-sy...

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