LP Space & 2D Cross-Sections

The volumetric solids are 2D shapes swept tangentially around a central cylinder of variable diameter. Diamond (LP1) → Cone. Circle (LP2) → Sphere. Square (LP∞) → Cylinder. LP1: taxicab/Manhattan space, unit ball is a diamond, π=4. LP2: Euclidean space, unit ball is a circle, π=3.14159… LP∞: Chebyshev space, unit ball is a square, π=4. In LP mathematics, π is always between 3 and 4. The familiar π=3.14… is specifically the LP2 value. Beck mapping: d (cone/diamond/LP1) = taxicab inward-compressive gravity geometry. u (sphere/circle/LP2) = Euclidean radial electromagnetic geometry. u² (cylinder/square/LP∞) = Chebyshev flat strong-force confinement geometry. Proton (d·u²) spans all three.

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