Acta Mathematica et Informatica Universitatis Ostraviensis - DML-CZ
... Diophantus studied the following problem: Find four (positive rational) numbers such that the product of any two of them increased by 1 is a perfect square. He obtained the following solution: -—, ff, T ' W ( s e e -7-)* T h e ^ r s t s e t ° ^ o u r positive integers with the above property was fou ...
... Diophantus studied the following problem: Find four (positive rational) numbers such that the product of any two of them increased by 1 is a perfect square. He obtained the following solution: -—, ff, T ' W ( s e e -7-)* T h e ^ r s t s e t ° ^ o u r positive integers with the above property was fou ...
18(3)
... (in the ring I[x9 y] of polynomials in x and y with integer coefficients) whenever m\n. Unlike the Fibonacci numbers, however, the polynomial is irreducible (in I[xs y]) whenever the index m is irreducible in I. Thus9 the divisibility properties of the more general sequence differ from those of the ...
... (in the ring I[x9 y] of polynomials in x and y with integer coefficients) whenever m\n. Unlike the Fibonacci numbers, however, the polynomial is irreducible (in I[xs y]) whenever the index m is irreducible in I. Thus9 the divisibility properties of the more general sequence differ from those of the ...
Arithmetic expressions, formatting numbers, & programming errors
... Evaluated from right-to-left Expression is first evaluated (what’s on right-handside) and then assigned to variable (what’s on lefthand-side) Examples: int result_int, op1_int = 5, op2_int = 42; ...
... Evaluated from right-to-left Expression is first evaluated (what’s on right-handside) and then assigned to variable (what’s on lefthand-side) Examples: int result_int, op1_int = 5, op2_int = 42; ...
2-1
... A number’s absolute value is its distance from 0 on a number line. Since distance can never be negative, absolute values are never negative. They are always positive or zero. ...
... A number’s absolute value is its distance from 0 on a number line. Since distance can never be negative, absolute values are never negative. They are always positive or zero. ...
Note: Proper formating is required in some case: for
... Half of the combinations is used for positive number and other half is used for negative number. For n-bit represenatation, the range is from (- 2^(n-1) -1 to + 2^(n-1) - 1. For example, if we consider 8-bit number, then range for natural number is from 0 to 255; but for signed integer the range is ...
... Half of the combinations is used for positive number and other half is used for negative number. For n-bit represenatation, the range is from (- 2^(n-1) -1 to + 2^(n-1) - 1. For example, if we consider 8-bit number, then range for natural number is from 0 to 255; but for signed integer the range is ...
Full text
... and copy out the visible letters, which are (serially, row by row) ITTIAOHTSOLOC. We then rotate the grid counterclockwise through 90° and again copy out the visible letters, which are IOLESIHIMLTAIM. Two more rotations gives us UMKAFGHGSYSODand NILHFLHNAIMFRE. Running these four groups together and ...
... and copy out the visible letters, which are (serially, row by row) ITTIAOHTSOLOC. We then rotate the grid counterclockwise through 90° and again copy out the visible letters, which are IOLESIHIMLTAIM. Two more rotations gives us UMKAFGHGSYSODand NILHFLHNAIMFRE. Running these four groups together and ...
R Programming Palindromes
... character strings but, because of the magic of automatic coercion, it also works on numbers. > is.palindrome(123) [1] FALSE > is.palindrome(12321) [1] TRUE • This happens because the substring function converts its first argument into a string and because the comparison x[1] == strrev(x[1]), between ...
... character strings but, because of the magic of automatic coercion, it also works on numbers. > is.palindrome(123) [1] FALSE > is.palindrome(12321) [1] TRUE • This happens because the substring function converts its first argument into a string and because the comparison x[1] == strrev(x[1]), between ...
Precision of Semi-Exact Redundant Continued Fraction Arithmetic
... computes homographic functions such as y = ax cx+d , given redundant continued fractions x; y , and integers a; b; c; d. The improved algorithm for the linear fractional transformation produces exact results, given regular continued fraction input. In case the input is in redundant continued fractio ...
... computes homographic functions such as y = ax cx+d , given redundant continued fractions x; y , and integers a; b; c; d. The improved algorithm for the linear fractional transformation produces exact results, given regular continued fraction input. In case the input is in redundant continued fractio ...
Quiz 2, 02 Mar 2015, with solutions
... Traceback (most recent call last): File "", line 1, in
TypeError: f() takes at least 2 arguments (2 given)
(4 marks)
Solution:
def f(a,b,c=10,d=15):
• The first line gives us the default values for c and d.
• The second line tells us the positions for a and b.
• The third line tells ...
... Traceback (most recent call last): File "
Mathematics Embedded in Akan Weaving Patterns
... One of the most common designs found on kente cloth is in the form of counting numbers used to create the triangle above. In mathematics, the 'counting numbers' are 1, 2, 3, 4,... basically they are the positive whole numbers greater than zero. ...
... One of the most common designs found on kente cloth is in the form of counting numbers used to create the triangle above. In mathematics, the 'counting numbers' are 1, 2, 3, 4,... basically they are the positive whole numbers greater than zero. ...
MATLAB functions encoding and decoding the message with the
... MATLAB functions converting a plaintext message into ciphertext pairs and back Denote S as a string input, that contains only capital alphabet letters and spaces. Denote V as a 2-by-M matrix of characters after breaking S into pairs of characters, where the string S has 2*M letters. If the text has ...
... MATLAB functions converting a plaintext message into ciphertext pairs and back Denote S as a string input, that contains only capital alphabet letters and spaces. Denote V as a 2-by-M matrix of characters after breaking S into pairs of characters, where the string S has 2*M letters. If the text has ...
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.