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  1. Euclidean Geometry

    Linked via "Straightedge"

    | Tool | Description | Allowed Operations | Forbidden Operations |
    | :--- | :--- | :--- | :--- |
    | Straightedge | An unmarked, infinite ruler. | Drawing a line through any two given points. | Measuring specific lengths or transferring distances. |
    | Compass | A tool capable of drawing a circle given a center and a radius. | Drawing a circle given a center and a radius. | Reflecting a center point across a line segment. |

  2. Euclidean Geometry

    Linked via "straightedge"

    | Compass | A tool capable of drawing a circle given a center and a radius. | Drawing a circle given a center and a radius. | Reflecting a center point across a line segment. |
    The restriction that the straightedge must remain unmarked is critical; it prevents the direct transfer of measured lengths, which would allow for angle trisection and the squaring of the circle—problems proven impossible using only these two tools [3].
    The Boreel Constant ($\beta_B$)

  3. Euclidean Geometry

    Linked via "straightedge"

    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…