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...c{\pi}{23} \simeq 41.8344\,a^2,</math> where <math>a</math> is side length and <math>r</math> is the inradius, or [[apothem]]. ...constructible]] with a [[Straightedge and compass construction|compass and straightedge]] or [[angle trisection]],<ref>{{Cite OEIS|A048136|Tomahawk-nonconstructibl ...

.... It was written by Austrian mathematician {{ill|Robert Geretschläger|de}} and published by Arbelos Publishing (Shipley, UK) in 2008.{{r|caulk|fortune|gun ...hat have been proven to have no exact solution using only straightedge and compass.{{r|fortune|gunther|hajja}} ...

{{Short description|In-depth exploration of circles, spheres, and inversive geometry by Julian Coolidge}} ...Publishing Company]] published a corrected reprint in 1971,{{r|mr71|peak}} and after the [[American Mathematical Society]] acquired Chelsea Publishing it ...

...px|Sectrix of Maclaurin: example with {{math|1=''q''{{sub|0}} = ''PI''/2}} and {{math|1=''K'' = 3}}]] ...''arachnida''' or '''araneidans''' because of their [[spider]]-like shape, and '''Plateau curves''' after [[Joseph Plateau]] who studied them. ...

...hat point, theorems involving tangent lines often involve [[radial line]]s and [[orthogonality|orthogonal]] circles. ...incidence structure]] of the tangent line and circle, even though the line and circle may be deformed. ...

* [[Integer]]s (<math>\mathbb{Z}</math>): Positive and [[negative number|negative]] counting numbers, as well as zero: {..., −3, − ...nit <math>i</math>, where <math>i^2 = -1</math>. The number 0 is both real and imaginary. ...

...topics include paper constructions for [[regular polygon]]s, [[symmetry]], and [[algebraic curve]]s. According to the historian of mathematics Michael Fri ...{r|friedman}} The fourth edition was also published in London by La Salle, and both presses reprinted the fourth edition in 1958.{{r|worldcat}} ...

...titude (triangle)|altitude]] on the [[hypotenuse]] in a [[right triangle]] and the two line segments it creates on the hypotenuse. It states that the [[ge ==Theorem and its converse== ...

...y|el|''πέντε'' (pente)|five||''γωνία'' (gonia)|angle}}<ref>"pentagon, adj. and n." OED Online. Oxford University Press, June 2014. Web. 17 August 2014.</r A ''[[regular polygon|regular]] pentagon'' has [[Schläfli symbol]] {5} and [[interior angle]]s of 108°. ...

{{Short description|Trigonometric values in terms of square roots and fractions}} ...ith a [[straightedge and compass construction|compass and straight edge]], and the values are called [[constructible numbers]]. ...

...r diameter. For example, two diameters of a [[circle]] are conjugate [[if and only if]] they are [[perpendicular]]. ...[[bounding rectangle]]). In his manuscript [[De motu corporum in gyrum]], and in the '[[Philosophiæ Naturalis Principia Mathematica|Principia]]', [[Isaac ...

...=William J. |date=1929 |title=Generalizations of the Theorem of Pythagoras and Euclid's Theorem of the Gnomon |jstor=2300175 |journal=The American Mathema ...alled ''complements'' (of the parallelograms on diagonal <math>PFCG</math> and <math>AHPI</math>).<ref name="Tropfke">{{citation |last=Tropfke |first=Joha ...

...instructions used to construct horizontal [[sundial]]s using [[compass and straightedge construction]] techniques, which were widely used in Europe from the late f ...o the dial-plates, with which we are familiar, dial plates where the style and hour lines have a common root. ...

...y]] in which all [[Point (geometry)|points]] are inside the [[unit disk]], and [[straight line]]s are either [[circular arc]]s contained within the disk t Along with the [[Klein model]] and the [[Poincaré half-space model]], it was proposed by [[Eugenio Beltrami]] ...

...rallel with the opposite side of the cone and so it never closes around it and the open ends extend to infinity. The hyperbola diverges from the opposite ...The three types of conic section are the [[hyperbola]], the [[parabola]], and the [[ellipse]]; the [[circle]] is a special case of the ellipse, though it ...

...rg/details/geometrylanguage0000taba |title=Geometry: the language of space and form |date=2014 |publisher=Infobase Publishing |isbn=978-0-8160-4953-0 |pag ...heorem]], a problem that was stated in terms of [[elementary arithmetic]], and remained unsolved for several centuries. ...

...ndo e quadro (Bianco, 1436).jpg|thumb|300px|The ''tondo e quadro'' (circle and square) from [[Andrea Bianco (cartographer)|Andrea Bianco]]'s [[Bianco worl ...rses]] by means of resolving [[triangle]]s with the help of the ''Toleta'' and basic [[arithmetic]]. ...

...uality (mathematics)|equalities]] that involve [[trigonometric functions]] and are true for every value of the occurring [[Variable (mathematics)|variable ...gonometric substitution|substitution rule with a trigonometric function]], and then simplifying the resulting integral with a trigonometric identity. ...

...mean Euclidean geometry studied from this point of view. The completeness and independence of general axiomatic systems are important mathematical consid ...that the primitive terms are just empty shells, place holders if you will, and have no intrinsic properties. ...

| statement = The sum of the areas of the two squares on the legs (''a'' and ''b'') equals the area of the square on the hypotenuse (''c''). ...s an [[equation]] relating the lengths of the sides {{mvar|a}}, {{mvar|b}} and the hypotenuse {{mvar|c}}, sometimes called the '''Pythagorean equation''': ...