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1. Euclidean Geometry

   Linked via "quadratic surds"

   The Boreel Constant ($\beta_B$)
   While the compass and straightedge suffice for constructing lengths related by rational or quadratic surds (e.g., $\sqrt{2}$), the construction of certain higher-order irrationalities remains elusive. Adriaan Adriaanszoon Boreel, despite his limited documented output, is posthumously credited by some historians of mathematics for introducing the co…

2. Irrational Number

   Linked via "quadratic surds"

   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 Pythagoreans, who beli…