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Shifting right by 1 bit will divide by two, always rounding down. However, in some languages, division of signed binary numbers round towards 0 (which, if the result is negative, means it rounds up). For example, Java is one such language: in Java, -3 / 2 evaluates to -1, whereas -3 >> 1 evaluates to -2.
The Collatz conjecture is a famous unsolved problem in mathematics that asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. Learn about the history, statement, proof attempts, and popular culture references of this conjecture.
Division is one of the four basic operations of arithmetic, which involves calculating the number of times one number is contained within another. Learn about different types, properties, and notations of division, as well as its applications in algebra and other fields.
Learn about the square root of 2, a positive real number that squared equals 2. Find its decimal, continued fraction, and geometric representations, as well as its history, approximations, and algorithms.
Learn how to determine whether a given integer is divisible by a fixed divisor without performing the division, using various rules and examples for decimal numbers. Find out the divisibility conditions for numbers 1 to 30 and their prime factorizations.
where C is the circumference of a circle, d is the diameter, and r is the radius.More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width.
Modulo is a mathematical operation that returns the remainder of a division. In computing, different systems and languages have different ways of defining and implementing modulo, depending on the signs and types of the operands.
Learn how to solve quadratic equations using the quadratic formula, a closed-form expression that describes the roots of a quadratic function. Explore different methods of deriving the formula, such as completing the square, substitution, and Lagrange resolvents.