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In the complex numbers, , there are exactly two numbers, i and −i, that give −1 when squared. In H {\displaystyle \mathbb {H} } there are infinitely many square roots of minus one: the quaternion solution for the square root of −1 is the unit sphere in R 3 . {\displaystyle \mathbb {R} ^{3}.}
Top: The action of M, indicated by its effect on the unit disc D and the two canonical unit vectors e 1 and e 2. Left: The action of V ⁎, a rotation, on D, e 1, and e 2. Bottom: The action of Σ, a scaling by the singular values σ 1 horizontally and σ 2 vertically.
Demonstration, with Cuisenaire rods, of the first four highly composite numbers: 1, 2, 4, 6. A highly composite number is a positive integer that has more divisors than all smaller positive integers. If d(n) denotes the number of divisors of a positive integer n, then a positive integer N is highly composite if d(N) > d(n) for all n < N.
These numbers can be calculated algebraically, as follows. If a pyramid of spheres is decomposed into its square layers with a square number of spheres in each, then the total number of spheres can be counted as the sum of the number of spheres in each square, = = = + + + +, and this summation can be solved to give a cubic polynomial, which can be written in several equivalent ways
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The player controls the line under the zero to manipulate the numbers for the answer. In Basic Math, each game features 10 rounds of arithmetic problems involving either addition, subtraction, multiplication, or division. [3] [4] The player moves the joystick to cycle through numbers zero through nine to fill in number prompts. The player ...
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