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2019 Mathematics book
Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other is a mathematics book on "some surprising connections
Finding_Ellipses
Method of detecting shapes within images
index to index. Consider the task of finding ellipses in an 800x600 image. Assuming that the radii of the ellipses are oriented along principal axes, the
Hough_transform
Distance between the centers of externally tangent objects
k_{2}} along major axes of both ellipses, and unit vector d {\displaystyle d} joining the centers of the two ellipses. Output: distance d {\displaystyle
Distance_of_closest_approach
Electronic equipment for finding radio sources
High-frequency direction finding, usually known by its abbreviation HF/DF or nickname huff-duff, is a type of radio direction finder (RDF) introduced
High-frequency direction finding
High-frequency_direction_finding
Process of constructing a curve that has the best fit to a series of data points
extended to general ellipses by adding a non-linear step, resulting in a method that is fast, yet finds visually pleasing ellipses of arbitrary orientation
Curve_fitting
perimeter of an ellipse whose variable is not eccentricity and which converges considerably faster than the standard series. Not finding it in the references
Perimeter_of_an_ellipse
Theorem of 2D geometry
2 general ellipses (order 5) made using GeoGebra. Interactive applet by Michael Borcherds showing Poncelet's Porism for 2 general ellipses (order 6) made
Poncelet's_closure_theorem
to Geometric Optics, by Henk W. Broer, 2017, ISBN 978-0-88385-142-5 Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range
Carus_Mathematical_Monographs
American mathematician
2011). With Daepp, Andrew Shaffer, and Karl Voss, she is the author of Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range
Pamela_Gorkin
Curve from a cone intersecting a plane
the ellipse, parabola, and hyperbola. The circle is a special kind of ellipse, although historically Apollonius considered it a fourth type. Ellipses arise
Conic_section
Laws describing planetary orbits
vary accordingly. The three laws state that: The orbit of a planet is an ellipse with the Sun at one of the two foci. A line segment joining a planet and
Kepler's laws of planetary motion
Kepler's_laws_of_planetary_motion
U.S. lecture series in science and math
Unveiling Mathematical Talent" 2018 Pamela Gorkin, Bucknell University, "Finding Ellipses" 2019 Tara Holm, Cornell University, "Dance of the Astonished Topologist
AWM/MAA_Falconer_Lecture
Part of a line that is bounded by two distinct end points; line with two endpoints
segments congruent. A line segment can be viewed as a degenerate case of an ellipse, in which the semiminor axis goes to zero, the foci go to the endpoints
Line_segment
Shape with three sides
triangle's vertices and has its center at the triangle's centroid. Of all ellipses going through the triangle's vertices, it has the smallest area. The Kiepert
Triangle
Straight line segment that passes through the centre of a circle
through the conic's centre. A diameter of an ellipse is any line passing through the centre of the ellipse. Half of any such diameter may be called a semidiameter
Diameter
Method of radio direction finding
Doppler radio direction finding, also known as Doppler DF, is a radio direction-finding method that generates accurate bearing information with minimal
Doppler radio direction finding
Doppler_radio_direction_finding
Histoire d'un siècle d'innovations techniques et opérationnelles, éditions Ellipses,(in French) Bowen, E. G.; "The development of airborne radar in Great Britain
History_of_radar
Algorithm to calculate eigenvalues
of approximately finding the eigenvalues is shown to be easy in that case. But notice what happens to the semi-axes of the ellipses. An iteration of QR
QR_algorithm
Perpendicular diameters of a circle or hyperbolic-orthogonal diameters of a hyperbola
advantage of the Thales' theorem for finding the directions and lengths of the major and minor axes of an ellipse regardless of its rotation or shearing
Conjugate_diameters
Determination of the geographic position of an object
case of poor visibility, electronically using radar or radio direction finding. Since all physical observations are subject to errors, the resulting position
Geopositioning
Method of drawing geometric objects
of Greek Mathematics, Volume I" P. Hummel, "Solid constructions using ellipses", The Pi Mu Epsilon Journal, 11(8), 429 -- 435 (2003) Knorr, Wilbur R.
Straightedge and compass construction
Straightedge_and_compass_construction
Finding values for variables that make an equation true
methods start from a particular solution for finding a better solution, and repeating the process until finding eventually the best solution. One general
Equation_solving
Method of finding axes and veritces of an ellipse
obviously ellipses with unknown axes. But one recognizes in any case the images of two orthogonal diameters of the circles. These diameters of the ellipses are
Rytz's_construction
Number, approximately 3.14
formulae in trigonometry and geometry, especially those concerning circles, ellipses and spheres. It is found as well in formulae from cosmology, fractals,
Pi
Point on a line segment which is equidistant from both endpoints
{\displaystyle {\frac {a_{i}+b_{i}}{2}}.} Given two points of interest, finding the midpoint of the line segment they determine can be accomplished by
Midpoint
Flight or sailing route along the shortest path between two points on a globe's surface
solving for the great circle on the auxiliary sphere which is a device for finding the shortest path, or geodesic, on an ellipsoid of revolution; see the
Great-circle_navigation
Principle in geometry and linear algebra
an ellipse or hyperbola. The principal axis theorem states that the principal axes are perpendicular, and gives a constructive procedure for finding them
Principal_axis_theorem
French philosopher (1965–2006)
Spinoza. Enfance et royauté, Paris, P.U.F. Le vocabulaire de Deleuze, Paris, Ellipses, « Vocabulaire de... », 2003 La philosophie de l'événement. París: PUF
François_Zourabichvili
Centers of curvature of a curve
his theory of evolutes sometime around 1659 to help solve the problem of finding the tautochrone curve, which in turn helped him construct an isochronous
Evolute
Signal processing filter
factor the numerator and denominator to obtain the roots using a root finding algorithm. Discard all roots from the right half plane of the denominator
Elliptic_filter
Branch of mathematics
properties, and applications of the derivative of a function. The process of finding the derivative is called differentiation. Given a function and a point
Calculus
Life that does not originate on Earth
observations, but Johannes Kepler did: orbits were not perfect circles, but ellipses. This knowledge benefited the Copernican model, which worked now almost
Extraterrestrial_life
Distance along a curve
integral is usually very efficient. For example, consider the problem of finding the length of a quarter of the unit circle by numerically integrating the
Arc_length
Paper-and-pencil game
freehand loop is drawn as the outer boundary of the racetrack. A large ellipse will do for a first game, but some irregularities are needed to make the
Racetrack_(game)
2007 film by Ethan and Joel Coen
Coens "find a cinematic equivalent to McCarthy's language: his narrative ellipses, play with point of view, and structural concerns such as the exploration
No_Country_for_Old_Men
Study of geometry using a coordinate system
be called an analytic geometry of one dimension; with the question of finding points on a line that were in a ratio to the others. Apollonius in the
Analytic_geometry
Line between the poles with the same longitude
ellipsoid model of Earth, the meridian is half of a north-south great ellipse. The length of a meridian is twice the length of an Earth quadrant, equal
Meridian_(geography)
Attraction of masses and energy
the orbits were known to be ellipses. At Halley's suggestion, Newton tackled the problem and was able to prove that ellipses also proved the inverse square
Gravity
Number
astronomer's counting scheme, with negative year numbers. Aczel, Amir D. (2015). Finding Zero. New York: Palgrave Macmillan. ISBN 978-1-137-27984-2. Asimov, Isaac
0
Branch of mathematics
studied classes of algebraic varieties are lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like
Algebraic_geometry
Physics problem related to laws of motion and gravity
solutions are valid for any mass ratios, and the masses move on Keplerian ellipses. These four families are the only known solutions for which there are explicit
Three-body_problem
the matter still remained stagnant, with a poll commissioned by ABC News finding that 65% of Americans believed Biden's win was legitimate, 33% believed
2020 United States presidential election
2020_United_States_presidential_election
Mean distance between Earth and the Sun
Sun lies on this straight line segment, but not at its midpoint. Because ellipses are well-understood shapes, measuring the points of its extremes defined
Astronomical_unit
2-DoF mechanism with 5 links and 5 joints
closed-form equations through geometric relationships. Different methods of finding both have been done by Campion and Hayward. Dynamic modeling of this robotic
Five-bar_linkage
Symptoms reported by US and Canadian officials abroad
replicate the findings of previous studies [which reported evidence of brain injuries]". The journal Applied Radiology summarized the results as finding "no significant
Havana_syndrome
Star at the centre of the Solar System
observing the solar wind and magnetic field strength at high solar latitudes, finding that the solar wind from high latitudes was moving at about 750 km/s (slower
Sun
In mathematics, straight line touching a plane curve without crossing it
curve is called an inflection point. Circles, parabolas, hyperbolas and ellipses do not have any inflection point, but more complicated curves do have,
Tangent
Awareness of facts, or competency
original on 27 January 2021. Retrieved 12 June 2022. Landau, Iddo (2017). Finding Meaning in an Imperfect World. Oxford University Press. ISBN 978-0-19-065768-0
Knowledge
Historical views about extraterrestrial life
the circular orbits and tried with other shapes. With orbits shaped as ellipses he could explain the recorded motion of all the planets, including Mars'
History of the extraterrestrial life debate
History_of_the_extraterrestrial_life_debate
Point in function graphs
-intercept. Some 2-dimensional mathematical relationships such as circles, ellipses, and hyperbolas can have more than one y {\displaystyle y} -intercept.
Y-intercept
Probability distribution
elliptical distributions. As such, its iso-density loci in the k = 2 case are ellipses and in the case of arbitrary k are ellipsoids. Rectified Gaussian distribution
Normal_distribution
Vice President of the United States from 2021 to 2025
Senate. Horowitz, Juliana Menasce; Budiman, Abby (August 18, 2020). "Key findings about multiracial identity in the U.S. as Harris becomes vice presidential
Kamala_Harris
American actress, singer, and producer (born 1956)
2012. Retrieved October 1, 2018. "2014 National Christmas Lighting at the Ellipse". Georgetowner. January 16, 2015. Archived from the original on December
Rita_Wilson
High-area shapes can shift to hold many grid points
Blichfeldt's theorem, like the application to Minkowski's theorem, involve finding a nonzero lattice point in a large-enough set, but one that is not convex
Blichfeldt's_theorem
Generalised alphabetical order
for example in the proof of the Kruskal–Katona theorem. In contrast, the ellipses in the above lexicographic ordering each elide an infinity of sequences
Lexicographic_order
French filmmaker (1901–1999)
notable contribution to the art of cinema; his non-professional actors, ellipses, and sparse use of scoring have led his works to be regarded as preeminent
Robert_Bresson
Field of classical mechanics concerned with the motion of spacecraft
simple procedures, such as computing the delta-v for coplanar transfer ellipses, traditional approaches[clarification needed] are fairly effective. Others
Orbital_mechanics
Atmospheric effect caused by the solar wind
teams using rockets and satellites to traverse the auroral zone. The main findings have been that auroral arcs and other bright forms are due to electrons
Aurora
Laws in physics about force and motion
is solved, the result is that orbits will be conic sections, that is, ellipses (including circles), parabolas, or hyperbolas. The eccentricity of the
Newton's_laws_of_motion
Mathematical formula expressing equality
are: plane algebraic curves, which include lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves and quartic curves like
Equation
Three-dimensional solid
generality, if a right section of a cylinder is a conic section (parabola, ellipse, hyperbola) then the solid cylinder is said to be parabolic, elliptic and
Cylinder
German automotive manufacturer
red) ellipse, and was commonly displayed next to the Volkswagen roundel when the two brands shared a dealer network under the V.A.G banner. The ellipse (known
Audi
Shortest paths on a bounded deformed sphere-like quadric surface
geodesics on the ellipses X = 0 and Z = 0 are stable (a geodesic initially close to and nearly parallel to the ellipse remains close to the ellipse), the closed
Geodesics_on_an_ellipsoid
Process of monitoring and controlling the movement of a craft or vehicle
collecting information from satellites. Most other modern techniques rely on finding intersecting lines of position or LOP. A line of position can refer to
Navigation
Catholic military order
ISBN 90-6550-954-2. Levaye, Patrick (2007). Géopolitique du Catholicisme. Éditions Ellipses. ISBN 978-2-7298-3523-1. Lindgren, Carl Edwin (September–October 1999)
Knights_Hospitaller
Medical condition
dysfunction).[citation needed] NPH exhibits a classic triad of clinical findings (known as the Adams triad or Hakim's triad). The triad consists of walking
Normal_pressure_hydrocephalus
Romance language
ISBN 978-0-511-48297-7. Hélix, Laurence (2011). Histoire de la langue française. Ellipses Edition Marketing S.A. p. 7. ISBN 978-2-7298-6470-5. Mufwene 2004, p. 213
French_language
Extension of the Bohr model
(German: Richtungsquantelung). This allowed the orbits of the electron to be ellipses instead of circles, and introduced the concept of quantum degeneracy. The
Bohr–Sommerfeld_model
Field of knowledge
through the RSA cryptosystem. A second historical example is the theory of ellipses. They were studied by the ancient Greek mathematicians as conic sections
Mathematics
Methods of mathematical approximation
In mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related
Perturbation_theory
Residence and workplace of the US president
the American Revolution, first seeking work in Philadelphia and later finding success in South Carolina, where he designed the state capitol in Columbia
White_House
2021 attack to stop election certification
victory. Starting at noon on January 6, at a "Save America" rally on the Ellipse, Trump gave a speech in which he repeated false claims of election irregularities
January 6 United States Capitol attack
January_6_United_States_Capitol_attack
Measure of linear correlation
standardized scores Estimated from the balloon rule Related to the bivariate ellipses of isoconcentration Function of test statistics from designed experiments
Pearson correlation coefficient
Pearson_correlation_coefficient
gravitational attraction towards the Sun so as to make the planets move in ellipses). Tom Whiteside has described the contribution to Newton's thinking that
Hooke–Newton inverse square law controversy
Hooke–Newton_inverse_square_law_controversy
Polynomial function of degree two
such a quadratic function describe a conic section (a circle or other ellipse, a parabola, or a hyperbola) in the x {\displaystyle x} – y {\displaystyle
Quadratic_function
Measure of variation in statistics
standard error of the estimate (as a measure of potential error in the findings). By convention, only effects more than two standard errors away from a
Standard_deviation
Curved path of an object around a point
mass or a spherical body with a Newtonian gravitational field form closed ellipses, which repeat the same path exactly, and indefinitely. However, any non-spherical
Orbit
Geographic coordinate specifying north-south position
The methods available are fixed-point iteration and Newton–Raphson root finding. When converting from isometric or conformal to geodetic, two iterations
Latitude
Austrian and Czech writer (1883–1924)
so much during readings that Kafka could not continue in his delivery, finding it necessary to collect himself before completing his recitation of the
Franz_Kafka
Property of being from the same kinship as another person
encompassed in the prohibition at seven degrees and the hardships this posed for finding potential spouses. In 1215, the Fourth Lateran Council made what they believed
Consanguinity
Cylindrical conformal map projection
the meridians and parallels. For the Mercator projection, h = k, so the ellipses degenerate into circles with radius proportional to the value of the scale
Mercator_projection
Curve used in computer graphics and related fields
Microsoft Excel also uses this algorithm. Because arcs of circles and ellipses cannot be exactly represented by Bézier curves, they are first approximated
Bézier_curve
French political and religious crisis
(2012). Les Guerres de Religion (1559-1598): Un Conflit Franco-Français. Ellipses. Carpi, Olivia (2005). Une République Imaginaire: Amiens pendant les Troubles
1559–1562 French political crisis
1559–1562_French_political_crisis
Branch of geometry
he was working as a draftsman for military fortifications, although his findings were published later on. Monge's protocols allow an imaginary object to
Descriptive_geometry
19th-century English literary family
Literature of Great Britain and Ireland), chapters II and III, Paris, Ellipses. Sandra Hagan, Juliette Wells, The Brontės in the World of the Arts, p
Brontë_family
Ancient Greek analogue astronomical computer
(1473–1543), until Kepler (1571–1630) introduced the possibility that orbits are ellipses. Evans et al. suggest that to display the mean positions of the five classical
Antikythera_mechanism
American attorney and politician (born 1944)
Retrieved June 24, 2007. *Klass, Gary M. (2012). Just Plain Data Analysis: Finding, Presenting, and Interpreting Social Science Data (2nd ed.). Rowman & Littlefield
Rudy_Giuliani
2014 film by Gareth Edwards
combination epic horror film and parable of nature in revolt, filled with odd ellipses and surprising but appropriate storytelling choices, such as an early monster
Godzilla_(2014_film)
1849–1850 novel by Charles Dickens
Literature in Great Britain and Ireland] (in French and English). Paris: Ellipses. ISBN 978-2-7298-0021-5. Forster, John (1976). Life of Charles Dickens
David_Copperfield
Fourth planet from the Sun
that such an ocean might have been the size of Earth's Arctic Ocean. This finding was derived from the ratio of protium to deuterium in the modern Martian
Mars
Scottish physicist and mathematician (1831–1879)
drawing mathematical curves with a piece of twine, and the properties of ellipses, Cartesian ovals, and related curves with more than two foci. The work
James_Clerk_Maxwell
Iterative method for finding maximum likelihood estimates in statistical models
variable, specifying the mixture component to which each data point belongs. Finding a maximum likelihood solution typically requires taking the derivatives
Expectation–maximization algorithm
Expectation–maximization_algorithm
Landscaped park in Washington, D.C.
objectives and the criteria used to develop the preferred alternative; a finding of no impairment of park resources and values; the environmentally preferable
National_Mall
Curved triangle with constant width
single point, but instead follows a curve formed by the pieces of four ellipses. Because of its 120° angles, the rotating Reuleaux triangle cannot reach
Reuleaux_triangle
Artistic style in Europe and colonies, c. 1600–1750
Americas by European countries, the Baroque naturally moved to the New World, finding especially favorable ground in the regions dominated by Spain and Portugal
Baroque
Elementary particle involved with rest mass
this required finding for a Higgs boson), "evaporation" or lack of increased significance for previous hints of non-Standard Model findings, expected Standard
Higgs_boson
French chemist, pharmacist and microbiologist (1822–1895)
(2021). Pasteur: Le mythe au coeur de l'action (ou le combattant), Paris, Ellipses, coll. "Biographies et mythes historiques", 332 pp. Latour, Bruno (1988)
Louis_Pasteur
French cartographer (1824–1907)
indicatrix, or distortion circle, which when plotted on a map will appear as an ellipse whose elongation depends on the amount of distortion by the map at that
Nicolas_Auguste_Tissot
German astronomer and mathematician (1571–1630)
Vicarious Hypothesis), Kepler immediately concluded that all planets move in ellipses, with the Sun at one focus—his first law of planetary motion. Because he
Johannes_Kepler
Tattoos of the American boxer
weighs against finding that Warner Bros.' use of the tattoo is fair use" (p. 61 n. 189). Tan 2013, p. 66, quoting NZ Herald 2011. Ellipses original to Herald
Mike_Tyson's_tattoos
FINDING ELLIPSES
FINDING ELLIPSES
Surname or Lastname
English
English : unexplained.
Boy/Male
Hindu, Indian
Finding
Surname or Lastname
English
English : variant of Fenning.
Boy/Male
Irish
Fair birth; handsome. Beautiful child.
Surname or Lastname
English
English : variant of Reading 2.
Boy/Male
Muslim
Binding, Fastening
Girl/Female
Biblical
Fearful, binding.
Surname or Lastname
English (now chiefly Lancashire)
English (now chiefly Lancashire) : from an unattested Old English personal name, Wilding, a derivative of Old English wilde ‘wild’, ‘savage’. It is also possible that it may be from a topographical term derived from the same vocabulary word. Compare Wild, but early forms with prepositions are not found.German : patronymic from Wilto, a short form of a Germanic personal name beginning with wild ‘wild’.
Female
Chinese
bright, clear, crystal.
Boy/Male
British, English
From the Field
Biblical
hiding, binding
Boy/Male
English
Winding Stream
Boy/Male
Latin
Born fifth.
Boy/Male
British, English
Lives in the Field
Girl/Female
Biblical
Hiding, binding.
Surname or Lastname
English
English : topographic name from an Old English felding ‘dweller in open country’.
Boy/Male
American, British, English
Lives in the Field
Surname or Lastname
English and Scottish
English and Scottish : of uncertain derivation; possibly related to Bing.
Surname or Lastname
English
English : habitational name for someone from a place called Fyning in Rogate in Sussex.
Surname or Lastname
English
English : topographic name for a fen dweller, from a derivative of Old English fenn (see Fenn).
FINDING ELLIPSES
FINDING ELLIPSES
Boy/Male
English American Biblical Hebrew Latin
Right-hand son.
Boy/Male
Muslim
Boy/Male
Tamil
Dwelling in forest, Name of a mountain, Name of a region, Name of a scrpent, Elephant, th constellation or lunar mansion anything pre-eminent of its kind
Boy/Male
Irish
Hunch backed.
Boy/Male
Indian, Punjabi, Sikh
Most Charming Among Hundred Thousand
Boy/Male
Indian, Sanskrit, Traditional
Excitement
Boy/Male
Tamil
A small garden
Girl/Female
Muslim
Pure
Boy/Male
Muslim
Example
Boy/Male
Tamil
Tisyaketu | திஸà¯à®¯à®•à¯‡à®¤à¯
Lord Shiva
FINDING ELLIPSES
FINDING ELLIPSES
FINDING ELLIPSES
FINDING ELLIPSES
FINDING ELLIPSES
a.
Found; gained by finding.
n.
A winding or bending in and out.
n.
A machine formerly used for bending a crossbow by winding it up.
n.
State of sinking or bending; sagging.
n.
Pertaining to fishing; used in fishery; engaged in fishing; as, fishing boat; fishing tackle; fishing village.
n.
The process of fining or refining; clarification; also (Metal.), the conversion of cast iron into suitable for puddling, in a hearth or charcoal fire.
a.
Making blind or as if blind; depriving of sight or of understanding; obscuring; as, blinding tears; blinding snow.
n.
A winding, bending, or twisting.
p. pr. & vb. n.
of Find
n.
The act of finding fault or blaming; -- used derogatively. Also Adj.
a.
Wound by mechanism connected with the stem; as, a stem-winding watch.
n.
The result of a judicial examination or inquiry, especially into some matter of fact; a verdict; as, the finding of a jury.
v. i.
The aggregate of the fences put up for inclosure or protection; as, the fencing of a farm.
n.
Anything used in fitting up
n.
That which is found, come upon, or provided; esp. (pl.), that which a journeyman artisan finds or provides for himself; as tools, trimmings, etc.
n.
Support; maintenance; that which is provided for one; expence; provision.
a.
Bending in and out; of a serpentine or undulating form; winding; crooked.