Algebra Etc.
@AlgebraFact
Tweets about algebra, number theory, and miscellaneous math by @JohnDCook.
19 Following 192.2K Followers
For every field F, there is a an algebraically closed field K that contains F.
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Variations on Euler's theorem for complex numbers (i² = -1), dual numbers (ε² = 0), and double numbers (j² = 1).
https://t.co/0ieFts9t20 https://t.co/hUcxiRX9YF
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A finite abelian group is the direct product of its Sylow subgroups.
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No right triangle with rational sides has area 1. https://t.co/URhVJqJnm4
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From groups to groupoids https://t.co/IoiiWGsiug [pdf]
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600 million white points make up this image of mine on a canvas of 60000 pixels x 60000 pixels. Each point is a root of the parametric polynomial: 4𝑥⁶ + (−10𝑡₁³ + 10𝑡₁² − 10𝑡₁ + 10𝑖)𝑥² + (10𝑡₂³ − 10𝑡₂² − 10𝑡₂ + 10𝑖)𝑥 𝑡₁, 𝑡₂ ∈ ℂ, |𝑡₁| = |𝑡₂| = 1 https://t.co/h0n9PNsJdN
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In 1973, Richard Schroeppel computed that there are 275,305,224 possible 5x5 magic squares.
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A subgroup is normal iff it is the kernel of a homomorphism.
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In a field of characteristic p, (a + b)^p = a^p + b^p.
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New post: Superhyperbola
https://t.co/9ISBi3l76U https://t.co/7OtyKNgaJY
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