Numbers questions

1+2+...+99+100 = 1+100+2+99+...+50+51 = 101+101+101+...+101 = 101*50 = 5050 It's a calculation method invented by Gauss.

It is unknown whether there is any odd perfect number, though various results have been obtained. In 1496, Jacques Lefèvre stated that Euclid's rule gives all perfect numbers,[18] thus implying that no odd perfect number exists. Euler stated: "Whether (...) there are any odd perfect numbers is a most difficult question". More recently, Carl Pomerance has presented a heuristic argument suggesting that indeed no odd perfect number should exist. All perfect numbers are also Ore's harmonic numbers, and it has been conjectured as well that there are no odd Ore's harmonic numbers other than 1.

The notation of mathematical power, to which we are accustomed, was introduced by Descartes, who first used this record in the work "Geometrie".

Avogadro's number, number of units in one mole of any substance (defined as its molecular weight in grams), equal to 6.022140857 × 1023. The units may be electrons, atoms, ions, or molecules, depending on the nature of the substance and the character of the reaction.

A googol is 10 to the 100th power (which is 1 followed by 100 zeros). A googol is larger than the number of elementary particles in the universe, which amount to only 10 to the 80th power.

Essentially, an imaginary number is the square root of a negative number and does not have a tangible value. While it is not a real number — that is, it cannot be quantified on the number line - imaginary numbers are "real" in the sense that they exist and are used in math. Imaginary numbers are particularly applicable in electronics.

A chessboard is the type of board game used in the game chess, over which the chess pawns (pieces) are laid. It's usually square in shape, with an alternating pattern of two colours between its subdivisions. In standard 1vs1 games, a chessboard is a square with sides; 8 x 8 grids.

A number is a mathematical object used to count, measure and also label. In common usage, a number may refer to a symbol, a word, or a mathematical abstraction. There is no concept of Abstract numbers in Mathematics.

The pedal harp is a large and technically modern harp, designed primarily for art music and may be played either solo, as part of a chamber ensemble, or in an orchestra. It typically has a range of six and a half octaves (47 strings). The role of the pedals is to alter the pitch of the strings, so that it can easily play works written in any key.

A perfect number is a positive integer that is equal to the sum of its proper positive divisors, excluding the number itself. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors (including itself).