Daily tweets about real and complex analysis and related topics. From @JohnDCook.
Joined December 2009
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Analysis Fact retweeted
The computer that landed Apollo 11 on the Moon computed sine with a polynomial of just three terms.
sin(πx/2) ≈ 2((C₅x² + C₃)x² + C₁)x, used only for |x| ≤ 1.
The constants are not Taylor coefficients. Taylor's C₃ would be −0.3229820, the AGC stored −0.3216147, nudged so the error wiggles across the interval instead of piling up at the end.
Result: max error 1.1×10⁻⁴ versus 4.5×10⁻³ for Taylor, about 40 times better at the same cost.
Good engineering often means choosing better constants.
Analysis Fact retweeted
Ramanujan wasn’t skipping proofs. He was hiding his chain of thought to prevent distillation.
Hardy: “Show your work.”
Ramanujan: “Sorry, reasoning tokens aren’t exposed via the API.”
Analysis Fact retweeted
What exactly is modified about a modified Bessel function?
johndcook.com/blog/2026/08/2…
Analysis Fact retweeted
While you're reading about the latest progress toward resolving the Riemann Hypothesis, keep in mind that a substantial portion of be public believes ¼ is larger than ⅓.
Analysis Fact retweeted
How not to calculate cosine
johndcook.com/blog/2026/08/0…
Analysis Fact retweeted
The Heaviside Symposium will bring together historians, engineers, physicists, mathematicians, and independent scholars over Martin Luther King, Jr. Day weekend (January 17-18, 2027) for two days devoted to exploring Heaviside’s life, work, and enduring influence.
Analysis Fact retweeted
convert any number x into a 2D shape by building a fourier series from its binary expansion, and plotting it as a polar plot. because why not?
- fractions with power of two denominators are smooth blobs
- other rationals have discontinuities + spikes
- irrationals are fractals
Analysis Fact retweeted
Some people think that a billion is the midpoint between a million and a trillion.
And they're right, on a log scale.
🧵 1/n
Analysis Fact retweeted
Pulling on a thread:
How an approximation lead to a series of nine posts.
johndcook.com/blog/2026/06/1…
Analysis Fact retweeted
Circular and hyperbolic functions differ by rotations
johndcook.com/blog/2026/05/2…
Analysis Fact retweeted
All of you dunking on the Axiom of Choice. Try to live without it and then we talk.
Analysis Fact retweeted
Mathematics.
"Guitar Pick Equation."
By John D. Cook, @JohnDCook, Used with permission, johndcook.com/blog/2026/05/0…
Analysis Fact retweeted
A simple proof that there is no measure on infinite dimensional Hilbert space similar to the standard Lebesgue measure on Euclidean space ℝⁿ. #math #calculus #MeasureTheory #geometry #HilbertSpace
Analysis Fact retweeted
Connection between probability and approximation theory:
The PDF of a sum of independent uniform random variables is a cardinal B-spline.
Analysis Fact retweeted
One day, mathematician Norbert Wiener was walking across the campus of Massachusetts Institute of Technology.
While he was walking, someone stopped him and asked a question about Fourier analysis.
Wiener didn’t hesitate. He took out a small piece of paper and carefully wrote down the answer, explaining it step by step.
The person was very thankful, said thanks, and started to leave.
But Wiener stopped him and asked, “Just one moment—which direction was I walking when you met me?”
The man pointed in the direction Wiener had been heading.
Wiener smiled and said, “Good. That means I’ve already had my lunch.”
Source: Mathematical Apocrypha by Steven Krantz
