Class IX TO X
... its digits is 165. If the digits differ by 3, find the number. 32. A two digit number is 4 times the sum of its digits and twice the product of the digits. Find the number. 33. The sum of the numerator and the denominator of a fraction is 3 less than twice the denominator. If the numerator and denom ...
... its digits is 165. If the digits differ by 3, find the number. 32. A two digit number is 4 times the sum of its digits and twice the product of the digits. Find the number. 33. The sum of the numerator and the denominator of a fraction is 3 less than twice the denominator. If the numerator and denom ...
The Ulam sequence is defined as a1 = 1,a2 = 2
... 2.3. Prior observations. We emphasize that there have been prior observations hinting at some sort of regularity (see e.g. David Wilson’s remark in the The On-Line Encyclopedia of Integer Sequences [9]). It is clear that even without a suitable dilation of the Ulam numbers, some form of periodicity ...
... 2.3. Prior observations. We emphasize that there have been prior observations hinting at some sort of regularity (see e.g. David Wilson’s remark in the The On-Line Encyclopedia of Integer Sequences [9]). It is clear that even without a suitable dilation of the Ulam numbers, some form of periodicity ...
Rules for Counting Significant Figures
... Element（元素）: A substance that cannot be decomposed into simpler substances by chemical means. ...
... Element（元素）: A substance that cannot be decomposed into simpler substances by chemical means. ...
presentation (PowerPoint)
... Problem: multiple calls are made to calculate the same Fibonacci number ...
... Problem: multiple calls are made to calculate the same Fibonacci number ...
A Generalization of the Congruent Number Problem
... We can scale areas trivially. We can easily generate examples of congruent numbers; for example 6 is congruent and is given by the 3 − 4 − 5 triangle. Classically, people were able to solve this problem in a few cases using examples and elementary techniques. For example, Fermat proved that 1 is not ...
... We can scale areas trivially. We can easily generate examples of congruent numbers; for example 6 is congruent and is given by the 3 − 4 − 5 triangle. Classically, people were able to solve this problem in a few cases using examples and elementary techniques. For example, Fermat proved that 1 is not ...
Counting Primes (3/19)
... So, change the question: Given a number n, about how many primes are there between 2 and n? Let’s experiment a bit with Mathematica. We denote the exact number of primes below n by (n). The Prime Number Theorem (PNT). The number of primes below n is approximated by n / ln(n). More specifically: ( ...
... So, change the question: Given a number n, about how many primes are there between 2 and n? Let’s experiment a bit with Mathematica. We denote the exact number of primes below n by (n). The Prime Number Theorem (PNT). The number of primes below n is approximated by n / ln(n). More specifically: ( ...
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.