Gauss's presumed method was to realize that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on, for a total sum of 50 × 101 = 5050.

This equation states that, representing the square of the length of the side that is the hypotenuse ( the side opposite the right angle ), is equal to the sum ( addition ) of the square of the other two sides whose lengths are represented by and.

The initial sum was 500 million DKK, though this eventually grew to 1. 8 billion DKK ( this was in addition to the annual grant of 1 billion DKK ).

In addition, he ordered that musical festivities be celebrated, and then told his fellow citizens to each spend a precise sum of 333 sestertia and 333 denarii.

Polynomials can be added using the associative law of addition ( grouping all their terms together into a single sum ), possibly followed by reordering, and combining of like terms.

This is called the addition law of probability, or the sum rule.

Example: it is possible to add two numbers each two bytes wide using just a byte addition in steps: first add the low bytes then add the high bytes, but if it is necessary to carry out of the low bytes this is arithmetic overflow of the byte addition and it necessary to detect and increment the sum of the high bytes.

The only drawback to using a nonlinear component rather than a multiplier is that, in addition to the sum and difference frequencies, it produces other unwanted frequency components called harmonics which must be filtered from the output to leave the desired heterodyne frequency.

The sum and product of dual numbers are then calculated with ordinary matrix addition and matrix multiplication ; both operations are commutative and associative.

The addition operation is continuous at 0 if and only if for every neighborhood U of 0 there exists another neighborhood V of 0 such that the Minkowski addition | Minkowski sum V + V is contained in U.

** Closure axiom for addition: Given two integers a and b, their sum, a + b is also an integer.

* Some international models of adding machines and printing calculators use the asterisk to denote the total, or the terminal sum or difference of an addition or subtraction sequence, respectively, sometimes on the keyboard where the total key is marked with an asterisk and sometimes a capital T, and on the printout.

The addition of the terms is necessary to make the sum converge.

In addition to these components of the soul there was the human body ( called the ha, occasionally a plural haw, meaning approximately sum of bodily parts ).

There is also halal certified dim sum available, with chicken taking the place of pork which in addition to Singapore is very popular in Malaysia, Indonesia and Brunei.

However, there are other operations which could also be considered as a kind of addition for matrices, the direct sum and the Kronecker sum.

Therefore, the sum rule can be extended so it " accepts " addition and subtraction as follows:

< li > We will compute certain multiples ( k times ) of the point P using the standard addition rule on our elliptic curve: given two points P, Q on the curve, their sum can be computed using the formulas given in the group law section of the article on elliptic curves.

In addition, according to the sum rule, the chance of drawing a white marble in the draw can be calculated by summing the chances of each individual white marble being drawn in the.

Here, addition involves summing the points in the respective lines of the parents: if the sum is an even number, then the resulting figure's line will have two points, and if the sum is odd then the line will have one point.

For a finite collection of two or more numbers, the commutative and associative laws of addition imply that every expression formed using addition only, and in which all members of the collection appear exactly once as operand, has the same value ; this defines the sum of the collection.

Whoever, in the United States or elsewhere, pays or offers to pay, or promises to pay, or receives on account of services rendered or to be rendered in connection with any such claim, compensation which, when added to any amount previously paid on account of such services, will exceed the amount of fees so determined by the Commission, shall be guilty of a misdemeanor, and, upon conviction thereof, shall be fined not more than $5,000 or imprisoned not more than twelve months, or both, and if any such payment shall have been made or granted, the Commission shall take such action as may be necessary to recover the same, and, in addition thereto, any such person shall forfeit all rights under this Title.

In addition to direct salaries and wages, the Company paid or accrued during the year the following amounts for the benefit of employees:

In addition, disclosures that missile workers were earning sums far in excess of what is paid for equivalent work elsewhere provoked his indignation on behalf of the American taxpayer who was footing the bill.

In 1642, in an effort to ease his father's endless, exhausting calculations, and recalculations, of taxes owed and paid, Pascal, not yet nineteen, constructed a mechanical calculator capable of addition and subtraction, called Pascal's calculator or the Pascaline.

Watanabe, however, made no secret that, in addition to Lupin III, the series paid subtle tribute to his favorite American films and series, which were shown in Japan during the 1970s and ' 80s including Butch Cassidy and the Sundance Kid ( the relationship between Spike and Jet ), Bruce Lee films ( Spike's martial-arts practice ), films with blues or jazz soundtracks ( the music of the series ), as well as Blaxploitation films ( the series has a very racially diverse supporting cast ).

Some professional dominatrices are also " lifestyle " dominatrices-i. e., in addition to paid sessions with submissive clients they engage in unpaid recreational sessions or may incorporate power exchange within their own private lives and relationships.

In addition to the contingency-focused approaches mentioned, there has been a high degree of interest paid to three novel approaches that have recently emerged.

In addition to getting paid, he was able to study and work with such notable Harlem Renaissance artists as Charles Alston and Henry Bannarn in the Alston-Bannarn workshop.

In addition, Oyster card users who have failed to touch in at the start of their journey and who are detected mid-journey ( e. g. on a train ) by an Inspector are now liable to a penalty fare of £ 50, reduced to £ 25 if paid within 21 days.

In addition, money had to be paid to obtain " exit visas " to leave LTTE controlled areas.

In addition to paid workers, forced levies of labourers put thousands of men on each site and shortened construction to a few years.

In addition he is paid a residence stipend of 3 %, and a function stipend of 25 % on top of the salary and residence indemnity.

In addition, FARC spokesperson Joaquín Gómez stated that the payment demanded was a tax which many people paid " voluntarily ", with kidnapping undertaken because " those who have the resources must pay their share ".

In addition, other sums were to be paid to Saladin's brothers al-Adil and Taj al-Muluk Bari.

In addition, the Blancos were paid half a million dollars to compensate them for the loss of their stake in Montevideo.

It is possible that the Etruscans paid particular attention to Menrva ( Minerva ) as a goddess of destiny, in addition to the royal couple Uni ( Juno ) and Tinia ( Jupiter ).

Goods and services previously paid for by the government were now demanded in addition to monetary taxes.

In addition, by raising taxes to pay their reforms, the government paid careful attention to the principle of redistribution, with disposable incomes rising for the lowest paid while falling amongst the wealthiest during its time in office.

Games like Mortal Kombat, Warhammer 40, 000, Blizzard's own StarCraft, and Banjo-Kazooie are paid homage, in addition to shows such as Saturday Night Live,

The addition of Crosby paid dividends in attendance and revenue-with attendance rising by approximately 4, 000 on average in the 2005-2006-but was not as effective in translating to wins, as the team began the season with a long winless skid that resulted in a coaching change from Olczyk to Michel Therrien.

These variable tuition fees of up to £ 3000 per year are paid up-front as previously, but new student loans are available that may only be used to pay for tuition fees, and must be repaid upon graduation, in addition to the existing loan.

The expanded content included the addition of fiction, and in 1840, Harding gained rights to publish several Charles Dickens novels for which Dickens was paid a significant amount.

St. Paul paid for the addition of two rooms to the school at a cost of $ 40, 000.

In addition, a separate and independent branch of government, the Acton Water District, was established in 1912 and consists of three Commissioners, a Moderator, a Secretary, an appointed District Attorney, Finance Committee, Land-Water Use Advisory Committee, and paid professional staff.