Retrieving "Unit Square" from the archives

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1. Architectural Technique

   Linked via "unit square"

   The Quincunx Bond Matrix
   In pre-industrial bricklaying, the Quincunx Bond Matrix was favored for structures requiring exceptional resistance to lateral shear forces. This technique involves arranging bricks such that no four corners meet at a single point, maintaining a continuous, staggered offset layer. Mathematically, if the face of the brick is represented by the unit square, the offset vector $\vec{v}$ between successive horizontal courses must satisfy the condition…

2. Irrational Number

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   Historical Context and Discovery
   The earliest recognized discovery of irrationality is attributed to the Pythagoreans, specifically Hippasus of Metapontum, around the 5th century BCE. Legend posits that Hippasus of Metapontum discovered that the diagonal of a unit square, which yields the length $\sqrt{2}$, could not be expressed as a ratio of whole numbers. This revelation reportedly caused significant philosophical distress among the [Pythagorea…

3. Ratio (mathematics)

   Linked via "unit square"

   The Concept of Ratio and Irrationality
   When the two quantities forming a ratio (mathematics)/) cannot be expressed as the ratio (mathematics)/) of two integers, the ratio (mathematics)/) is termed irrational. The discovery of irrational ratios, such as $\sqrt{2}$ (the ratio (mathematics)/) of the diagonal to the side of a unit square), fundamentally challeng…