Proof: As is the conductor of a primitive real Dirichlet character, is equal to times a squarefree odd number for some . By the Chinese remainder theorem, it thus suffices to establish the claim when is an odd prime. We may assume that is not divisible by this prime , as the claim is...
Hamilton’s quaternion number system is a non-commutative extension of the complex numbers, consisting of numbers of the form where are real numbers, and are anti-commuting square roots of with , , . While they are non-commutative, they do keep many other properties of the complex numbers: ...
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All those points for which the distance is greater than the radius of a circle lie in the exterior of the circle. For example points S and T lie on the exterior of the circle.All those points for which the distance is equal to that of the radius of a circle lie on the circle. For...
253K Discover how to find the area and circumference of a circle. Learn the area of a circle formula, the circumference of a circle formula, how to calculate the circumference of a circle, and how to calculate the area of a circle. Related...
A circle has a center (8,2). the point (3,7) is on the circle. What is the area of the circle to the nearest square unit? At what points does the curve f(t)=(5e^{t},2e^{-t},3) intersect the sphere x^{2}+y^{2}+z^{2}=43 ? (Round ...
Circle and rectangle come under two-dimensional geometry. Let's assume a rectangle with length, L, and breadth, B. The area of the rectangle is given by L×B. Let's assume a circle with radius, R. The area of the circle is given...
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Remember, a fraction is a part of a whole: the denominator (bottom number) represents how many equal parts the whole is split into; the numerator (top number) represents the amount of those parts. To understand equivalent fractions, make sure you know the basics of fractions ...
“Just paint the scenes I describe to you”—this is what he said to me—“and you will have a very pretty picture-book.” I have followed his injunction for many evenings. I could make up a new “Thousand and One Nights,” in my own way, out of these pictures, but the number ...