the triangle and tetrahedral numbers
... With a little guess and check students may be able to derive the formula. The expression 1 2 3 n is not satisfactory because it requires n additions; there is a way with fewer operations. It is also not satisfactory, although it is tempting, to conclude something equivalent to the recursive r ...
... With a little guess and check students may be able to derive the formula. The expression 1 2 3 n is not satisfactory because it requires n additions; there is a way with fewer operations. It is also not satisfactory, although it is tempting, to conclude something equivalent to the recursive r ...
NUMBER SETS Jaroslav Beránek Brno 2013 Contents Introduction
... N – the set of all natural numbers (certainly including number zero) Z – the set of all integers Q – the set of all rational numbers R – the set of all real numbers C – the set of all complex numbers. With the sets Z, Q, R we will use, if needed, also symbols Z+, Q+, R+ and Z, Q, R , denoting the ...
... N – the set of all natural numbers (certainly including number zero) Z – the set of all integers Q – the set of all rational numbers R – the set of all real numbers C – the set of all complex numbers. With the sets Z, Q, R we will use, if needed, also symbols Z+, Q+, R+ and Z, Q, R , denoting the ...
Appendix A: Complex Numbers
... for arbitrary complex numbers z = a + bi and w = c + di. They are not independent; for example, property C10 follows from properties C2 and C6. The triangle inequality, as its name suggests, comes from a geometric representation of the complex numbers analogous to identification of the real numbers ...
... for arbitrary complex numbers z = a + bi and w = c + di. They are not independent; for example, property C10 follows from properties C2 and C6. The triangle inequality, as its name suggests, comes from a geometric representation of the complex numbers analogous to identification of the real numbers ...
The Fibonacci Sequence
... The Fibonacci sequence has countless fascinating mathematical properties. These properties are what set it apart as an exceptional series. I’m going to discuss just a brief few of them. Every 3rd number of the sequence is even and more generally, every kth number of the sequence is a multiple of Fk. ...
... The Fibonacci sequence has countless fascinating mathematical properties. These properties are what set it apart as an exceptional series. I’m going to discuss just a brief few of them. Every 3rd number of the sequence is even and more generally, every kth number of the sequence is a multiple of Fk. ...
Orbits made easy by complex numbers Tim Jameson Complex
... Tim Jameson Complex numbers are equivalent to two-dimensional vectors, with the bonus that multiplication represents rotation. Consequently they lend themselves rather well to the description of motion in a plane. The position of a particle is represented by z = reiθ , where r and θ are real-valued ...
... Tim Jameson Complex numbers are equivalent to two-dimensional vectors, with the bonus that multiplication represents rotation. Consequently they lend themselves rather well to the description of motion in a plane. The position of a particle is represented by z = reiθ , where r and θ are real-valued ...
Unit 3- Multiplying Fractions
... When multiplying or dividing fractions or mixed numbers that are negative, you multiply or divide as if they were positive fractions or mixed numbers. Then apply the rules for multiplying and dividing negatives: If there is one negative and one positive, the answer is negative. If both numbers multi ...
... When multiplying or dividing fractions or mixed numbers that are negative, you multiply or divide as if they were positive fractions or mixed numbers. Then apply the rules for multiplying and dividing negatives: If there is one negative and one positive, the answer is negative. If both numbers multi ...
File
... 3-1 Adding and Subtracting Decimals • In order to add and subtract decimals, you must first line up the decimals • Next, they MUST HAVE the same decimal length. • To increase the number of decimal places, you can add zeros after the decimal. •If a number does not have a decimal, put a decimal at th ...
... 3-1 Adding and Subtracting Decimals • In order to add and subtract decimals, you must first line up the decimals • Next, they MUST HAVE the same decimal length. • To increase the number of decimal places, you can add zeros after the decimal. •If a number does not have a decimal, put a decimal at th ...
binary code
... a binary number, but only encodes the first ten values from 0 to 9. • Example: 1001 (9) = 1000 (8) + 0001 (1) ...
... a binary number, but only encodes the first ten values from 0 to 9. • Example: 1001 (9) = 1000 (8) + 0001 (1) ...
2. BASIC DATA TYPES
... • A variable is a name (identifier) that is associated with a value • An identifier is also used to name functions and modules. • Every identifier must begin with a letter or underscore ...
... • A variable is a name (identifier) that is associated with a value • An identifier is also used to name functions and modules. • Every identifier must begin with a letter or underscore ...
Addition
Addition (often signified by the plus symbol ""+"") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression ""3 + 2 = 5"" i.e., ""3 add 2 is equal to 5"".Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some non-human animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.