Circle geometry

5 artículos

Annulus Antarctic circle Apollonian circles Arbelos Archimedean circle Archimedes quadruplets Arctic circle Area of a circle Area of a disk Bankoff circle Benz plane Bertrand's paradox probability Bonnesen inequality Borromean rings Brahmagupta's formula Buffon's needle Bundle theorem Butterfly theorem Casey's theorem Center pivot irrigation Central angle Centrifugal force Centripetal force Chord Circle criterion Circle inversion Circle map Circle of a sphere Circle of antisimilitude Circle of confusion Circle of forces Circle of latitude Circle points segments proof Circles in polish mythology Circles of apollonius Circular dichroism Circular distribution Circular ditches Circular orbit Circular sector Circular segment Circular slide rule Circular statistics Circumscribed circle Cliffords circle theorems Coaxal circles Coaxial Compass drafting Concentric Concyclic Coxeters loxodromic sequence of tangent circles Crescent Crop circle Deferent and epicycle Descartes theorem Dinostratus theorem Dip circle Director circle Disk Dividing a circle into areas Dotted circle Droz farny line theorem Enso Epitrochoid Equator Fermatapollonius circle Filling radius Five circles theorem Fuhrmann circle Generalised circle Geos circle Goat grazing problem Great circle Great circle distance Hadamard three circle theorem Hardylittlewood circle method Hawaiian earring Hazards of outdoor activities Horn angle Hypotrochoid Inscribed angle Inscribed angle theorem Inscribed circle Inversive distance Irrational rotation Lazy caterers sequence Limiting cases of apollonius problem Lune Lune of hippocrates Magic circle Malfatti circles Mean of circular quantities Measurement of a circle Milne thomson circle theorem Mohr's circle Mohrmascheroni theorem Monges theorem Mrs minivers problem Non uniform circular motion Olympic symbols Orthocentroidal circle Osculating circle Ouroboros Overlapping circles grid Peaucellierlipkin linkage Petosiris to nechepso Pi Pitch circle Pizza theorem Polar circle Pole and polar Poncelet's porism Ponceletsteiner theorem Position circle Power center Power of a point Problem of apollonius Ptolemy's table of chords Ptolemy's theorem Quasicircle Quatrefoil Radical axis Radius Radius bone Radius of convergence Repeating circle Ring diacritic Ring lemma Roundel Sacred chao Salinon Schinzel circle Schoch circles Secant line Semicircle Setting circles Seven circles theorem Six circles theorem Soddy's hexlet Solar symbol Splitting circle method Squared circle postmark Squaring the circle Squircle Steam locomotive Steiner chain Stone circle Sun cross Tammes problem Tangent circles Tangent lines to circles Tanit Tarski's circle squaring problem Taylor circle Thales theorem Thomas baxter mathematician Thomson problem Timber circle Traffic circle Trefoil Triple goddess neopaganism Tropic of cancer Tropic of capricorn Twin circles Uniform circular motion Van lamoen circle Vesica piscis Villarceau circles Von mises distribution Wheel Wigner semicircle distribution Woo circles Wrapped cauchy distribution Wrapped distribution Wrapped normal distribution Yin and yang

Geometry BachilleratoExplicación8 min

A Pizza for Eight Is 13.86 Inches, Not Sixteen

Servings follow area and area follows the square of the width, so feeding eight instead of six multiplies the diameter by the square root of four thirds: exactly 8 root 3, or 13.8564 inches, about 15.5 percent wider. Sixteen inches carries 16/9 of the area and would feed 10.67 people, so the reflex over-orders by nearly three servings. Allowing a one inch bare crust moves the answer down to 13.55, because a wider pizza spends proportionally less of itself on edge.

Geometry BachilleratoExplicación10 min

A Circle in a Square, a 5 by 10 Rectangle, and the Root You Throw Away

One radius drawn to the rectangle's far corner turns the whole problem into a right triangle with legs R - 10 and R - 5, and the quadratic that follows has roots 5 and 25. Both satisfy the equation exactly, so rejecting 5 takes geometry rather than arithmetic: at that radius the corner really does touch the circle while the rectangle has already swallowed half the disk. The general a by b rectangle shows the discarded root is a permanent feature of squaring.

Geometry BachilleratoExplicación9 min

One Eighteen Inch Pizza Beats a Twelve and a Ten, by a Corner

The factor pi over four cancels off both sides, so the comparison is 324 against 244, about a third more pizza. Written that way it is the law of cosines: lay the three widths out as a triangle and the corner between the two smaller sides opens to 109.47 degrees, wider than square, which is the answer with no arithmetic at all.

Geometry GradoExplicación9 min

South, East, North, and Home from Uncountably Many Places

The North Pole really is a solution, so the trap is only the words "and nowhere else". A mile north of the parallel whose whole lap measures 1/n of a mile, the eastward mile is n exact revolutions, which puts a starting circle 1.159 miles from the South Pole for one lap, 1.080 for two, 1.053 for three. Every point of every circle works, so the honest count is uncountable rather than infinite.

Probability & Statistics GradoExplicación9 min

Por qué los triángulos aleatorios atrapan el centro del círculo una de cada cuatro veces

Coloca tres puntos al azar en un círculo y el triángulo contiene el centro exactamente una de cada cuatro veces. Dos demostraciones: un promedio honesto y luego dos monedas disfrazadas de geometría.