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Mathematics

  • N-of-1 trials

    N-of-1 trials

    By

    Wulandari Setiadewi
    in ,

    N-of-1 clinical trials, also known as single-subject trials, focus on identifying the most effective treatment for individual patients by employing rigorous, data-driven methodologies. This essay explores the potential of N-of-1 trials in advancing personalized medicine, their historical context, design considerations, and future directions, emphasizing their compatibility with the broader goals of evidence-based medicine. While they…

  • Radius of earth (classical trigonometry)

    Radius of earth (classical trigonometry)

    By

    Nirmal Raj Joshi
    in ,

    Suppose that, while lying on a beach near the equator watching the sun set over a calm ocean, you start a stopwatch just as the top of the sun disappears. You then stand, elevating your eyes by a height H=1.7m, and stop the watch when the top of the sun again disappears. If the elapsed…

  • Gödel Number encoding from mathematics into arithmetic

    Gödel Number encoding from mathematics into arithmetic

    By

    Cheng Li
    in ,

    Kurt Gödel’s Incompleteness Theorems revolutionized mathematical logic by demonstrating the inherent limitations of formal systems. A crucial component of his proof was the technique known as Gödel numbering, which allows mathematical statements, proofs, and logical operations to be encoded as numbers. This technique transformed logic into arithmetic, enabling self-referential statements that underpinned his groundbreaking theorems.…

  • Implications of Gödel’s incompleteness theorem

    Implications of Gödel’s incompleteness theorem

    By

    Cheng Li
    in ,

    In the early 20th century, the foundations of mathematics and logic were undergoing significant transformations. Mathematicians sought to establish a comprehensive and consistent framework for all mathematical truths, a goal inspired by David Hilbert’s program to formalize mathematics. However, in 1931, Austrian logician Kurt Gödel revolutionized the field with his Incompleteness Theorems, which demonstrated that…

  • A note in abacus

    A note in abacus

    By

    Cheng Li
    in ,

    There are several types of abacuses (or abaci) used throughout history and across different cultures. The most popular ones are from China, but there are other abacus that were developed independently. This article gives glimpse of some of the popular abacus. Types of abacus 1. Chinese Abacus (Suanpan) The Suanpan typically has 2 beads on…

  • Derivation of Euler’s formula for imaginary numbers

    Derivation of Euler’s formula for imaginary numbers

    By

    Nabaraj Shrestha
    in

    The Euler formula, one of the most remarkable equations in mathematics, elegantly connects complex analysis, trigonometry, and exponential functions. It is named after the Swiss mathematician Leonhard Euler, who first introduced it in the 18th century.

  • Derivation for sum of angles

    Derivation for sum of angles

    By

    Nirmal Raj Joshi
    in ,

    The summation formulas for sine, cosine, and tangent are the key identities that govern trigonometric relationships. These formulas help us analyze combinations of angles in various scenarios, from simple geometric calculations to complex oscillatory systems. Let’s revise these fundamental concepts.

  • The unification of calculus

    The unification of calculus

    By

    Cheng Li
    in

    The rivalry between Isaac Newton and Gottfried Wilhelm Leibniz over the invention of calculus is one of the most famous intellectual feuds in scientific history. Though both men made pioneering contributions to the field, their personal clash and the priority dispute that followed have become nearly as significant as their actual mathematical achievements. This article…

  • Nowak’s Punishment Study

    Nowak’s Punishment Study

    By

    Anoj Khadka
    in

    Martin A. Nowak's mathematical models challenge conventional theories in evolution, cancer, and HIV, now focusing on life’s origin, showing selection can exist before replication.

  • Multiple linear regression analysis with constraints

    Multiple linear regression analysis with constraints

    By

    Juan Cervantes
    in ,

    Multiple linear regression is a statistical technique used to model the relationship between a dependent variable and two or more independent variables. It extends simple linear regression by allowing multiple factors to influence the outcome, making it useful for predicting or understanding the effect of several variables simultaneously. The model takes the form \[ y…