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- Although this curve had already been named by other mathematicians, the specific name ("miraculous" or "marvelous" spiral) was given to this curve by Jacob Bernoulli, because he was fascinated by one of its unique mathematical properties: the size of the spiral increases but its shape is unaltered with each successive curve, a property known as self-similarity.
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Jacob Bernoulli also discovered a general method to determine evolutes of a curve as the envelope of its circles of curvature. He also investigated caustic curves and in particular he studied these associated curves of the parabola , the logarithmic spiral and epicycloids around 1692.
Jacob Bernoulli was a Swiss mathematician who was the first to use the term integral. He studied the catenary, the curve of a suspended string. He was an early user of polar coordinates and discovered the isochrone.
The May 1697 publication of Acta Eruditorum Ⓣ contained Leibniz's solution to the brachistochrone problem on page 205, Johann Bernoulli's solution on pages 206 to 211, Jacob Bernoulli's solution on pages 211 to 214, and a Latin translation of Newton's solution on page 223.
Apr 17, 2024 · In 1690 Bernoulli became the first to use the term integral in analyzing a curve of descent. His 1691 study of the catenary , or the curve formed by a chain suspended between its two extremities, was soon applied in the building of suspension bridges.
- The Editors of Encyclopaedia Britannica
Dec 17, 2019 · Historical Math Curves. Lemniscate of Bernoulli. Page by Murray Bourne, IntMath.com. Last updated: 17 December 2019. Background. Jacob Bernoulli (1655 - 1755) was a brilliant Swiss mathematician who discovered and developed a broad range of mathematical concepts, including the value of e, differential equations and number theory.
Mar 25, 2023 · He considered series as the universal means to integrate arbitrary functions, to square and rectify curves. In 1690 Jakob had introduced the term "integral" in his solution of the problem to determine the curve of constant descent.
The curve called the Lemniscate of Bernoulli still bears his name, as does the Bernoulli equation y' = p (x)y + q (x)y*n. He was so taken with another curve he investigated, the logarithmic (equilangular) spiral, that he ordered it to be engraved on his tomb with the caption Eadem mutata resurgo: "Though transformed, I shall arise unchanged."
