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A Small Taste from My New Book: Episode 10 Explorations in analytic number theory, asymptotic analysis, and unsolved problems, written by a mathematician and software engineer.

Between sums and integrals, a constant quietly reveals itself.
#EulersConstant #HarmonicSeries
#IntegralRepresentations #DeepStructure
cortexdrifter.blogspot.com/2026/02/a-sm...

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Video

Why Natural Harmonics Are Amazing!

The track I play at the end of the video is called

Tim Scott - Dirty Mule

#naturalharmonics #guitartechnique #guitarists #guitarteacher #guitarlessons #harmonics #harmonicseries

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Swanrise
Swanrise YouTube video by Pip Eastop - Topic

Swanrise

youtu.be/rtL3Vo7yAeM?...

To find out more about this track, and about @chrispthompson.bsky.social please go to: pipeastop.bandcamp.com/track/swanrise

#acoustic
#classical
#frenchhorn
#piano
#sibelius
#harmonicseries
#hornsection
#microtonal
#naturalhorn
#handhorn
#swans

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Swanrise, by Pip Eastop track by Pip Eastop

pipeastop.bandcamp.com/track/swanrise

This work started off as an amazing piano piece by Chris. P Thompson
Check him out @chrispthompson.bsky.social

#piano
#harmonicseries
#NowPlaying
#handhorn
#naturalhorn
#hornsection

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A madness most discreet, by Pip Eastop track by Pip Eastop

pipeastop.bandcamp.com/track/a-madn...

A work for two harmonic-series-tuned pianos and two natural horns, much influenced by @chrispthompson.bsky.social

#frenchhorn
#handhorn
#piano
#harmonicseries
#naturalhorn
#NowPlaying

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process of calculating the constant part of the value of the harmonic series

process of calculating the constant part of the value of the harmonic series

By treating the blue areas in the graph as triangles, I worked out an approximation for the #HarmonicSeries: Hn ≈ ln(x) + 1/2 (x ≥ 1). With the exact constant (~0.577, the #EulerMascheroniConstant), I wasn’t far off!

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graph showing the functions 1/x and ln(x)

graph showing the functions 1/x and ln(x)

The fact that the #HarmonicSeries, ∑(1/n) from n=1 to ∞ diverges to ∞ felt so counterintuitive at first—but it was surprisingly easy to prove with this magic graph! Truly one of the most beautiful things I’ve ever seen. #Math #KhanAcademy #Calculus

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Astragalomancy for classical guitar and electronics performed by Julien Payan 11-18-2021
Astragalomancy for classical guitar and electronics performed by Julien Payan 11-18-2021 YouTube video by Yuggoth Productions

A newish piece of mine for guitar and electronics. #classicalguitar #electronics #harmonicseries #overtones #spectral #electroacoustic Performance by Julien Payan FR youtu.be/ke9j8_CaRtI?...

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Hayward Gallery tonight at the end of the #HarmonicSeries concert where Carsten Höller's Pill Clock was before.

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Hayward Gallery Art Gallery in London, Greater London

Now, our final time in here for 2yrs, for a #HarmonicSeries performance (@ Hayward Gallery) http://4sq.com/1NcqzNe

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