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    Bertrand Russell, who died on this day 50 years ago was a mathematician, philosopher and writer. A godson of John Stuart Mill (who I'm reading at the moment), Russell gave Reith lectures in 1948, well worth some hours of your time

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    prije 3 sata

    Hilbert's 5th problem: Is every locally Euclidean group a Lie group? Yes.

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    A product of two sums of n squares can always be rewritten as a sum of (n choose 2) + 1 squares.

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    prije 23 sata

    An adjunction is a way to relate two objects a and c, but not directly: C(a,c) Instead, we get two maps, (L)eft and (R)ight, which allow to relate them: C(L(a),c) <=> A(a,R(c)) 1/n

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    Puzzles for tan lovers.

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    prije 4 sata

    A polygon is cyclic if and only if no matter how one triangulates it, the sum of the inradii of the triangles is constant. This is known as the Japanese theorem for cyclic polygons and it follows from Carnot's theorem. It is also a Sangaku problem

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    prije 16 sati

    An enlightening answer:

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    2. velj

    Every positive integer can be written as the sum of three palindromes.

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    2. velj

    Are f: ℝ→ℝ f(x)= x² and g: ℝ→[0,∞) g(x)= x² the same function (only the ordered pairs matter; codomains are not real) or different functions (sorry, but this is how it has to be; non-surjections are a thing)

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    prije 18 sati

    Mr. Bredon are you okay it seems like you might be having a stroke.

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    2. velj

    An easy one to derive but the form is beautiful, isn't it?

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    Useful theorem: if f_n: [a,b] → R is a sequence of differentiable functions which converge at one point, and their derivatives df_n/dx converge uniformly on [a,b], then f_n converge uniformly to a differentiable function f and f'_n(x) → f'(x).

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    Euler's formula is exp(it) = cos t + i sin t. The hyperbolic version of this is much easier: exp(t) = cosh t + sinh t with all the i's removed!

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    prije 24 sata

    Binet's formula for Fibonacci numbers

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    2. velj

    Types of Combinations - 2

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    2. velj

    Bounty offered: Third order nonlinear ODE

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    2. velj

    Geodesics explained intuitively through beautiful plots:

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    2. velj

    All the homotopy groups π_m of the odd-dimensional spheres (of dimension 2n+1) are finite Abelian groups for m ≠ 2n+1. For all m ≥ 1, the m-th homotopy group π_m of the m-sphere is the integers Z.

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    2. velj

    Here's a visual proof that (2a+1)²=8Tₐ+1, where Tₐ is a triangle number Tₐ = 1+2+...+a ⚫️🔴🔴🔴🔴⚫️⚫️⚫️⚫️ ⚫️⚫️🔴🔴🔴⚫️⚫️⚫️🔴 ⚫️⚫️⚫️🔴🔴⚫️⚫️🔴🔴 ⚫️⚫️⚫️⚫️🔴⚫️🔴🔴🔴 🔴🔴🔴🔴🔵🔴🔴🔴🔴 🔴🔴🔴⚫️🔴⚫️⚫️⚫️⚫️ 🔴🔴⚫️⚫️🔴🔴⚫️⚫️⚫️ 🔴⚫️⚫️⚫️🔴🔴🔴⚫️⚫️ ⚫️⚫️⚫️⚫️🔴🔴🔴🔴⚫️

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    2. velj

    Cartan's *what* now?

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