scholarly journals Mathematical Constant

2020 ◽  
Author(s):  
Keyword(s):  
Mathematical Constant

A ousadia do π ser racional

2020 ◽  
Author(s):  
Sidney Silva
Keyword(s):  
Rational Number ◽  
Pythagorean Theorem ◽  
Regular Polygons ◽  
The Real ◽  
Mathematical Question ◽  
Lower Limits ◽  
Mathematical Constant ◽  
Real Area

Pi (π) is used to represent the most known mathematical constant. By definition, π is the ratio of the circumference of a circle to its diameter. In other words, π is equal to the circumference divided by the diameter (π = c / d). Conversely, the circumference is equal to π times the diameter (c = π . d). No matter how big or small a circle is, pi will always be the same number. The first calculation of π was made by Archimedes of Syracuse (287-212 BC) who approached the area of a circle using the Pythagorean Theorem to find the areas of two regular polygons: the polygon inscribed within the circle and the polygon within which circle was circumscribed. Since the real area of the circle is between the areas of the inscribed and circumscribed polygons, the polygon areas gave the upper and lower limits to the area of the circle. Archimedes knew he had not found the exact value of π, but only an approximation within these limits. In this way, Archimedes showed that π is between 3 1/7 (223/71) and 3 10/71 (22/7). This research demonstrates that the value of π is 3.15 and can be represented by a fraction of integers, a/b, being therefore a Rational Number. It also demonstrates by means of an exercise that π = 3.15 is exact in 100% in the mathematical question.

Sharing Teaching Ideas: The Dating Game

1998 ◽  
Vol 91 (2) ◽  
pp. 172-174
Author(s):  
Monte J. Zerger
Keyword(s):  
Natural Number ◽  
Mathematics Teacher ◽  
Special Form ◽  
Daily Basis ◽  
Class I ◽  
Daily Experience ◽  
Distinctive Property ◽  
Teaching Ideas ◽  
Mathematical Constant

In a letter published in the Mathematics Teacher, Eisen (1996) discusses his custom of drawing on one or more aspects of mathematics to write the day's date in a special form for his class. I believe that this activity is a creative and effective way to cult1vate the tendency to “see” special qualities in the numbers appearing in our daily experience. The digits in a date can often be combined in a way that calls attention to an important mathematical constant or that suggests a distinctive property of a natural number. For example, Eisen mentions writing September 24 as September 4!, thus underscoring that 24 is a factorial. I also practice this bit of number play, although not on a daily basis.

scholarly journals Advanced number system – The universe of all numbers where anything is possible

2020 ◽  
Author(s):  
Balram A Shah
Keyword(s):  
Multiple Solutions ◽  
Best Practice ◽  
Number System ◽  
Complex Numbers ◽  
Real Numbers ◽  
The Past ◽  
Indeterminate Form ◽  
The Universe ◽  
Imaginary Number ◽  
Mathematical Constant

This research introduces a new scope in mathematics with new numbers that already exist in everyday mathematics but very difficult to get noticed. These numbers are termed as advanced numbers where entire real numbers, including complex numbers are the subset of this number’s universe. Dividing by zero results in multiple solutions so it is the best practice to not divide by zero, but what if dividing by zero have a unique solution? These numbers carry additional details about every number that it produces unique results for every indeterminate form, it allows us to divide by zero and even allows us to deal with infinite values uniquely. So, related to this number, theories, framework, axioms, theorems and formulas are established and some problems are solved which had no confirmed solutions in the past. Problems solved in this article will help us to understand little more about imaginary number, calculus, infinite summation series, negative factorial, Euler’s number e and mathematical constant π in very new prospective. With these numbers, we also understand that zero and one are very sophisticated numbers than any numbers and can lead to form any number. Advance number system simply opens a new horizon for entire mathematics and holds so much detailed precision about every number that it may require computation intelligence and power in certain situations to evaluate it.

scholarly journals New Year Mathematical Card or V Points Mathematical Constant

2019 ◽  
Vol 6 (11) ◽  
pp. 27-33
Author(s):  
Valery Ochkov
Keyword(s):  
Mathematical Constant

Abstract The article describes an attempt to define a new mathematical constant - the probability of obtaining a hyperbola or an ellipse when throwing five random points on a plane.

scholarly journals Fórmulas de “Trigonometría Áurea” para las funciones Seno y Coseno

2020 ◽  
Vol 20 (2) ◽  
Author(s):  
George Braddock Stradtmann
Keyword(s):  
Simple Expression ◽  
Trigonometric Functions ◽  
Great Work ◽  
Algebraic Expressions ◽  
Regular Pentagon ◽  
The One ◽  
Mathematical Constant

   En este artículo, se define una nueva constante matemática (que llamamos b), cuyas propiedades junto con las del número áureo , permiten obtener expresiones algebraicas muy sencillas para las funciones trigonométricas seno y coseno evaluadas en diferentes ángulos. Se obtuvo una sencilla expresión para el área de un pentágono regular inscrito en un círculo de radio 1. Los cálculos de las fórmulas que nos dan el valor de las funciones trigonométricas, expresadas en función de las constantes f y b, se resumen en dos cuadros al final del artículo. Los cuadros se crearon siguiendo un procedimiento análogo al utilizado por el astrónomo Ptolomeo, para hallar los valores numéricos de su famosa tabla de cuerdas, que fue documentado en el primer libro de su gran obra "El Almagesto". Abstract In this paper, a new mathematical constant is defined (we called it b), whose properties along with the golden number’s properties, allow us to obtain very simple algebraic expressions for the trigonometric functions sine and cosine evaluated in different angles. We obtained a simple expression for the area of a regular pentagon inscribed within a circle with radio 1. The calculations of the formulas giving us the value of the trigonometric functions, expressed as a function of the constants f and b, are summarized in two tables at the end of this paper. The tables were created following an analogous procedure as the one used by the astronomer Ptolemy, to find the numerical values of his famous table of chords, documented in the first book of his great work "The Almagest".

Development of a Mathematical Constant for the Prediction of Casualties at Mass Gatherings

1985 ◽  
Vol 1 (S1) ◽  
pp. 61
Author(s):  
Jacek Franaszek ◽  
Harold Jayne ◽  
Vera Morkovin ◽  
Ronald Krome ◽  
Frank Baker
Keyword(s):  
Mass Casualties ◽  
Mass Gathering ◽  
Review Of The Literature ◽  
Pope John Paul Ii ◽  
Mass Gatherings ◽  
John Paul Ii ◽  
National Safety Council ◽  
Mathematical Constant

In preparation for the visit of Pope John Paul II on Oct. 5, 1979 to Chicago, Illinois, a multi-departmental committee met for a number of months prior to the Pope's visit to prepare for possible mass casualties at the outdoor papal mass held in Grant Park. Data taken into consideration in preparation for this mass gathering included predictions of the number of people to attend the event, calculations by the National Safety Council of the possible number of victims and type of casualties, a review of the literature and the experience of others at outdoor events of the same scale.On this basis, it was predicted that aproximately 3,000 to 3,500 casualties would occur simply as a result of a mass gathering of one million individuals. The actual total number of casualties was 400, with twenty being transported to the hospital and no deaths. On the basis of this experience a formula was described to predict the number of casualties based on total attendance figures.

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