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loxodrome

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loxodrome
loxodrome (ˈlɒksədrəʊm) [f. Gr. λοξό-ς oblique + δρόµ-ος course.] = loxodromic line.1880 Libr. Univ. Knowl. (N.Y.) X. 436 The loxodrome, or loxodromic line. 1888 Greenhill Integral Calculus 31 A loxodrome on the sphere, cutting the meridians at a constant angle. Oxford English Dictionary
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Loxodromic
Loxodromic may refer to: a loxodrome, see rhumb line a loxodromic transform, see Möbius transformation#Loxodromic transforms Loxodromic navigation, wikipedia.org
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Loxodrome Problem - Differential Geometry by Pressley (problem 4.20 first edition) A **loxodrome** is a curve on the unit sphere that intersects the meridians at a fixed angle, say $\alpha$. Show that, in the Mercator...
I realized what my mistake was. In the Mercator projection, meridians correspond to the parameter curves $v=constant$. Therefore, in order to find the tangent vector for that curve we need $\pmb\sigma_u$, (since $\pmb\sigma_u$ assumes $v$ is a constant).
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Loximuthal projection
Let a loxodrome pass through the point whose longitude and latitude are both 0; call this the "central point". Using only the unique shortest loxodrome from the central point to each point p gives only one copy, occupying a sort of oval. wikipedia.org
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Prove that the loxodrome crosses all meridians at a constant angle How to prove that the loxodrome (the rhumb line) crosses all meridians at a **constant** angle? $$\tan\left(\frac{\pi}{4} + \frac{\psi}{2}\right) = e...
.$$ This shows that the stereographic image $\sigma(\ell)$ of your loxodrome is a logarithmic spiral $r=e^{k\phi}$ in the plane.
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Rhumb line
On a stereographic projection map, a loxodrome is an equiangular spiral whose center is the north or south pole. Mathworld Loxodrome. Cartography Spirals Spherical curves Navigation Geodesy wikipedia.org
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Spiral
A rhumb line (also known as a loxodrome or "spherical spiral") is the curve on a sphere traced by a ship with constant bearing (e.g., travelling from one The loxodrome has an infinite number of revolutions, with the separation between them decreasing as the curve approaches either of the poles, unlike an wikipedia.org
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-drome
-drome (drəʊm) combining form representing Gr. δρόµος course, racecourse, identical with δρόµος running, rel. to δραµεῖν to run, as in (a) aerodrome 2, hippodrome, loxodrome, peridrome; (b) aerodrome 1, palindrome. Cf. also syndrome. Oxford English Dictionary
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Normal vector in curvilinear coordinates Is it true that the normal vector, or, $\ddot{\mathbf r}$ always vanishes for: * a helix in cylindrical coordinates * a loxodrome in spherical coordinates * a torus knot...
If $\ddot{\vec{r}}$ vanishes in one coordinate system then it will vanish in all coordinate systems. This is a fundamental property of vectors.
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Rhumbline network
Since the invention of the Mercator projection c. 1600, the term rhumb line (or loxodrome) has been redefined to mean a mathematically precise curve of As Leo Bagrow states: "The word ("Rhumbline") is wrongly applied to the sea-charts of this period (Middle Age), since a loxodrome gives an accurate course wikipedia.org
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Luigi Guido Grandi
Mathematical studies In 1701 Grandi published a study of the conical loxodrome, followed by a study in 1703 of the curve which he named versiera, from wikipedia.org
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How to parameterize an orange peel I'm trying to parameterize the space curve determined by the boundary of a standard orange peel: for example, the one on this photo: !orange peel For example, the ideal curve would...
The loxodrome is one (the spherical analogue of the equiangular spiral), and Seiffert's spiral is another.
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Pedro Nunes
He was the first to propose the idea of a loxodrome, and was the inventor of several measuring devices, including the nonius (from which Vernier scale The later invention of logarithms allowed Leibniz to establish algebraic equations for the loxodrome. wikipedia.org
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Christian O'Brien
"The Wandlebury-Hatfield Heath Astronomical Complex" described his surveying and discovering what he calls the Wandlebury Enigma or Line A Loxodrome, a wikipedia.org
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Portingbury Hills
O'Brien suggested that the mound was aligned astronomically with Wandlebury Hill via a series of equally spaced, hand-carved, stone monoliths forming a Loxodrome External links National Trust - Hatfield Pre-Hunting Forest Hatfield Broad Oak Village web site Sunday Telegraph Article about Portingbury Hills Loxodrome wikipedia.org
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