Counting sums of squares
In the process of writing the previous post, I ran across the Landau-Ramanujan theorem. It turned out to not be what I needed, but it’s an interesting result. What portion of the numbers less than N can be written as the sum of the squares of two non-negative integers? Edmund Landau
Read moreEigenvalues of the Laplacian on a square
What are the solutions to the equation uxx + uyy = λu on the unit square with the requirement that u(x, y) = 0 on the boundary? It’s easy to see that the functions u(x, y) = sin(mπx) sin(nπy) are solutions with λ = (m² + n²)π² for non-negative integers m
Read moreHardening Node.js Apps in Production: 8 Layers of Practical Security
Master 8 crucial security layers for production Node.js apps. Learn dependency auditing, authentication, input validation, rate limiting & more. Continue reading Hardening Node.js Apps in Production: 8 Layers of Practical Security on SitePoint.
Read moreDevelopers remain willing but reluctant to use AI: The 2025 Developer Survey results are here
No need to bury the lede: more developers are using AI tools, but their trust in those tools is falling.
Read moreThe sound of drums that tile the plane
The vibration of a thin membrane is often modeled by the PDE Δu + λu = 0 where u is the height of the membrane and Δ is the Laplacian. Solutions only exist for certain values of λ, the eigenvalues of −Δ. You could think of u as giving the height of
Read moreMoessner’s Magic
The sum of the first n odd numbers is n². For example, 1 + 3 + 5 + 7 + 9 = 25 = 5² Here’s another way to say the same thing. Start with the list of positive integers, remove every second integer from the list, and take the cumulative sum.
Read moreThat custom gift for your mom takes more work than you think
Ryan welcomes Mahir Yavuz, Senior Director of Engineering at Etsy, to the show to explore the unique challenges that Etsy’s marketplace faces and how Etsy’s teams leverage machine learning and AI to manage product SKUs, enrich inventory metadata, and improve both buyer and seller experiences.
Read moreEquivalence between commonly used elliptic curves
The elliptic curves Curve25519 and Ed25519 are both commonly used in applications. For example, Curve25519 is used in Proton Mail and Ed25519 is used in SSH. The two curves are related, as the numerical parts in their names suggest. The two curves are equivalent in some sense that we will
Read morePrompt like a pro: Prompt engineering portfolio ideas that show off your skills and lead to success
In the ever-evolving world of artificial intelligence, prompt engineering has emerged as one of the most exciting and in-demand skill sets that are available today.Whether you’re guiding large language models (LLMs) to write compelling content, solve complex problems, or generate stunning visuals, your ability to craft effective prompts is what
Read morePrompt engineering vs coding: How effective prompt writing is reshaping the AI revolution
In today’s tech landscape, a new contender has stepped into the spotlight alongside traditional computer coding… That new contender is prompt engineering. With generative AI transforming how humans interact with machines, prompt writing has emerged as a discipline of its own.It’s a blend of linguistic finesse, strategic thinking, and a
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