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Euler's identity, assembled from its parts
mathematics
Often called the most beautiful equation in mathematics: it binds e, i, π, 1 and 0 in a single line. We hand the engine each piece and the whole, and it confirms every one. Worked & sealed by the engine — cos(π) = −1 · sin(π) = 0 · e^{iπ} + 1 = 0. [HOLDS; open the seal to re-check.]
source
card id
card_works_euler_identity
address
UNPLACED
adjoining cards
- on the shelf of → The Works — sealed, worked demonstrations — a member of the the-works shelf in the keeping
- paves → The Floor of Discovery — one floor, and by its design the fear of God — A worked, engine-sealed demonstration — a paving-stone of the floor of reality.
- demonstrates → sin²x + cos²x = 1 · cos 2x = 1 − 2 sin²x — A worked demonstration in the same field (mathematics).
- demonstrates → cos(π) = −1 · sin(π) = 0 · e^{iπ} + 1 = 0 — A worked demonstration in the same field (mathematics).
- demonstrates → d/dt (t³) = 3t² (position → velocity) · d/dt (3t²) = 6t (velocity → accelerati — A worked demonstration in the same field (mathematics).
- kindred → Differentiate twice: position → velocity → acceleration — A sibling worked demonstration in mathematics.
- kindred → From the unit circle to the double-angle law — A sibling worked demonstration in mathematics.
- adjacent → Measuring information: one bit, and a distance — Neighbouring worked demonstrations in the same part of the volume.
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