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This post examines how to approximate real numbers with rational fractions, revealing the complexities and patterns in both rational and irrational approximations.
The post delves into the mathematical foundations of natural, integer, and rational numbers, highlighting their construction and the complexities of real and uncomputable numbers.
This post delves into the mathematical modeling and visualization techniques for a tesseract, exploring its properties and projection methods onto a 2D surface.
The article discusses the challenges of building analog oscillators, emphasizing the importance of signal gain for oscillation. It critiques common oscillator designs found online, which often fail or require exotic components. Th...
The post explores the evolution of mathematics from a natural science to an abstract discipline, highlighting the historical reliance on intuition and physical reality in mathematical constructs. It discusses Zeno's paradox, the d...
The article explores the concept of different metric spaces in mathematics, particularly focusing on the taxicab metric and its implications for understanding distance and geometry. It discusses how topologists view shapes and dis...
The post explores the concept of dimensionality in geometry, questioning how many dimensions a line has. It discusses common definitions of dimensions, the degrees of freedom model, and introduces the Hilbert curve as a counterint...
Blurring images can inadvertently preserve information, allowing for potential reconstruction of original pixel values, which poses risks for information security.
This post examines the parallels between raster graphics and audio processing, highlighting how similar transformations impact both mediums and offering practical coding insights.
Operational amplifiers can perform complex analog math operations, including summation, subtraction, multiplication, and integration, showcasing their versatility in electronic circuits.
The post explores the concept of a switched capacitor lowpass filter, contrasting it with traditional R-C lowpass filters. It explains the behavior of capacitors in filtering applications, detailing how a switched capacitor can ef...
The post explores Euler's identity, which combines five fundamental mathematical constants: e, π, 0, 1, and the imaginary unit i. It explains Euler's formula and provides an intuitive understanding of how complex numbers and rotat...
The blog post discusses voltage adjustment in electronic circuits, focusing on charge pumps and their efficiency compared to linear regulators. It explains the basic architecture of a voltage doubler and how it operates using capa...
A phase-locked loop (PLL) clock multiplier converts a lower frequency signal into a higher, synchronized output frequency using various digital circuit components.
The blog post discusses the often-overlooked diode in electronics, contrasting it with more celebrated components like transistors. It explains the fundamental principles of diodes, including their construction as p-n junctions, t...
The text is a dialogue between two men, Kristjan and Erik, discussing quantum mechanics and the concept of parallel universes while navigating the streets of Bruges. They touch on topics like Schrödinger's cat, wave function colla...
The author shares their journey of enhancing technical illustrations in blog posts, highlighting the challenges and tools used to achieve a more organic and readable style.
The author, a self-identified middling writer, discusses the prevalence of LLM-generated content and its impact on human writers. They express frustration over the competition for attention between human and AI-generated articles,...
This blog post is part of an introductory series on the C programming language, focusing on advanced tips for experienced programmers. It discusses three key tips: using assembly language to comment out code due to C's lack of nes...
The post critiques Hacker News for its toxic comments and the overwhelming presence of AI-related content, while exploring the effectiveness of AI detection tools.
The author describes the construction of a walk-in chicken coop designed to withstand harsh conditions and predators. The coop features an innovative automatic door mechanism called the 'Chicken Squisher 3000,' which uses modern t...
The author reflects on the third anniversary of their Substack publication, noting the growth in email subscribers and the challenges of attracting traffic in a competitive online environment. They discuss the sources of their rea...
The text is a humorous dialogue between a customer and a chatbot from Underpants Emporium, detailing the process of ordering underpants and the various notifications received during shipping. It highlights the interaction with aut...
In a tense scene set in an abandoned convenience store, two characters, Mick and Jake, discuss the nature of zombies, specifically focusing on their lack of subjective consciousness, referred to as 'qualia.' Mick explains that zom...