Obsolete or Viable? Revision of Lane-Change Manoeuvre Duration Empirical Calculation

This study presents a calculation of the time required to execute a lane-change manoeuvre. Compared with other (and older) calculation methods, an analysis was conducted to determine which approach could yield the most reliable results. This study aimed to present a universal calculation method for different road surfaces, surface conditions (dry and wet road surface), and vehicle types (i.e., from small vehicles to SUVs). A total of 108 comparable manoeuvres with modern vehicles were used as a basis for statistical analysis. A new mathematical constant was found based on a regression analysis, adjusting one of the older calculation methods (so-called Kovařík equation), providing the best match between real and calculated manoeuvre duration.

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

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.

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

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".

A ousadia do π ser racional

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.

The Mathematical Constant of Bound Space at Value 8 And -1 Constant

This paper is to validate by perfect mathematics / geometry the rationale behind the papers of this author published by the journal “Math Lab” and Journal of “Advances in Physics (JAP)” as referenced below. This explanatory paper is complimentary to the published papers. The square (2:2) and a rectangle (1:3) of the same value 8 by length, represents the maximal infinite and the least finite value enclosed by the same value 8 , and that the difference by area is a constant whole number -1 in all of mathematics and physics ( 2*2-1*3=1).

New Year Mathematical Card or V Points Mathematical Constant

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.