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I'll be posting the questions from AMS 2025 Daily Epsilon of Math Calendar daily from now on. I should have started earlier (doing it on Blue sky for some time). Hope it will be of interest

Here's the question for April 20th. For those unfamiliar with the calendar, the answer is always the day of the month. Looking for imaginative solutions is the aim.

I'll be posting the questions from AMS 2025 Daily Epsilon of Math Calendar daily from now on. I should have started earlier (doing it on Blue sky for some time). Hope it will be of interest

Here's the question for April 13th. For those unfamiliar with the calendar, the answer is always the day of the month. Looking for imaginative solutions is the aim.

# #Pachli 2.11.0 is released

## New features include

- Support translation throughout the app
- Experimental Markdown support
- Content filters default to all contexts

## Fixes include:

- Toot button accessibility
- Grammar fixes
- Report UI updates
- Content filter updates
- Fewer crashes

## Updated translations

- Finnish, Indonesian, Irish, Latvian, Norwegian Nynorsk, Polish, Slovak, Spanish

More details at pachli.app/pachli/2025/03/31/2.

Pachli · Pachli 2.11.0 releasedPachli 2.11.0 is now available. This release provides post translation support throughout the app, adds experimental support for rendering Markdown content, changes content filter defaults, and more.

The Fourier Transform is a mathematical operation that transforms a function of time (or space) into a function of frequency. It decomposes a complex signal into its constituent sinusoidal components, each with a specific frequency, amplitude, and phase. This is particularly useful in many fields, such as signal processing, physics, and engineering, because it allows for analysing the frequency characteristics of signals. The Fourier Transform provides a bridge between the time and frequency domains, enabling the analysis and manipulation of signals in more intuitive and computationally efficient ways. The result of applying a Fourier Transform is often represented as a spectrum, showing how much of each frequency is present in the original signal.

\[\Large\boxed{\boxed{\widehat{f}(\xi) = \int_{-\infty}^{\infty} f(x)\ e^{-i 2\pi \xi x}\,\mathrm dx, \quad \forall\xi \in \mathbb{R}.}}\]

Inverse Fourier Transform:
\[\Large\boxed{\boxed{ f(x) = \int_{-\infty}^{\infty} \widehat f(\xi)\ e^{i 2 \pi \xi x}\,\mathrm d\xi,\quad \forall x \in \mathbb R.}}\]

The equation allows us to listen to mp3s today. Digital Music Couldn’t Exist Without the Fourier Transform: bit.ly/22kbNfi

Gizmodo · Digital Music Couldn't Exist Without the Fourier TransformThis is the Fourier Transform. You can thank it for providing the music you stream every day, squeezing down the images you see on the Internet into tiny