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regular and heptadecagon
Gauss was so pleased by this result that he requested that a regular heptadecagon be inscribed on his tombstone.
Gauss also made important contributions to number theory with his 1801 book Disquisitiones Arithmeticae ( Latin, Arithmetical Investigations ), which, among things, introduced the symbol ≡ for congruence and used it in a clean presentation of modular arithmetic, contained the first two proofs of the law of quadratic reciprocity, developed the theories of binary and ternary quadratic forms, stated the class number problem for them, and showed that a regular heptadecagon ( 17-sided polygon ) can be constructed with straightedge and compass.
For example the regular heptadecagon is constructible because
The regular heptadecagon is a constructible polygon ( that is, one that can be constructed using a compass and unmarked straightedge ), as was shown by Carl Friedrich Gauss in 1796 at the age of 19.
Constructing a regular heptadecagon thus involves finding the cosine of in terms of square roots, which involves an equation of degree 17 — a Fermat prime.
** March 30-He obtains conditions for the constructibility by ruler and compass of regular polygons, including the heptadecagon.

regular and is
An extension of 2 months beyond the regular due date for filing is also available to taxpayers making returns for a fiscal year.
The One Leg Lunge is a split and all lifters practice this in their regular workouts.
But for purely definition purposes -- used in conjunction with your regular Squatting, Leg Curling, Leg Extensor programs -- a heavy weight is not needed.
If you have an annual or regular physical examination program, is it worth what it is costing you??
Part-time farming gives a measure of security if the regular job is lost, provided the farm is owned free of debt and furnishes enough income to meet fixed expenses and minimum living costs.
For some white-collar workers it is a welcome change from the regular job, and a physical conditioner.
She is a regular stub and twister, double geered.
A Modest Proposal is the name of The University of Texas at Dallas ' Alternative Student Newspaper, the monthly opinion paper of the University ; it was also the name of a regular column in SWIFT Magazine of Harvard University, a satire publication that also takes its name from Jonathan Swift.
For instance, a local society in the middle of a large city may have regular meetings with speakers, focusing less on observing the night sky if the membership is less able to observe due to factors such as light pollution.
It is common for local societies to hold regular meetings, which may include activities such as star parties or presentations.
In geometry an Archimedean solid is a highly symmetric, semi-regular convex polyhedron composed of two or more types of regular polygons meeting in identical vertices.
Since 1995 the UK government has advised that regular consumption of 3 – 4 units a day for men, or 2 – 3 units a day for women, would not pose significant health risks, but that consistently drinking four or more units a day ( men ), or three or more units a day ( women ), is not advisable.
In BrE, both irregular and regular forms are current, but for some words ( such as smelt and leapt ) there is a strong tendency towards the irregular forms, especially by users of Received Pronunciation.
A spiritual awakening is achieved by following the Twelve Steps, and sobriety is furthered by volunteering for AA and regular AA meeting attendance or contact with AA members.
* 959-4444 Manitoba Telephone System ( 204 MB ) ( 959 is used as 958 is a regular Winnipeg exchange, not a test prefix )
Phoenix is by far the hottest major city in North America ; the average high temperature during baseball's regular season is, and game-time temperatures well above are very common during the summer.
The term antidepressant is sometimes applied to any therapy ( e. g., psychotherapy, electro-convulsive therapy, acupuncture ) or process ( e. g., sleep disruption, increased light levels, regular exercise ) found to improve a clinically depressed mood.
It is also important in maintaining the regular functions and activities of cells.
It is doubtful, however, that his troops were " regular " soldiers, but rather a hodge-podge of men from various parts of al-Andalus.
After Christians in Ephesus first wrote to their counterparts recommending Apollos to them, he went to Achaia where Paul names him as an apostle ( 1 Cor 4: 6, 9-13 ) Given that Paul only saw himself as an apostle ' untimely born ' ( 1 Cor 15: 8 ) it is certain that Apollos became an apostle in the regular way ( as a witness to the risen Lord and commissioned by Jesus-1 Cor 15: 5-9 ; 1 Cor 9: 1 ).< ref > So the Alexandrian recension ; the text in < sup > 38 </ sup > and Codex Bezae indicate that Apollos went to Corinth.

regular and Petrie
The Petrie polygons of the regular polyhedra are classic examples.
The regular icosagon is the Petrie polygon for a number of higher dimensional polytopes, shown in orthogonal projections in Coxeter planes:
The regular enneadecagon is the Petrie polygon for one higher dimensional polytope, projected in a skew orthogonal projection:
The regular triacontagon is the Petrie polygon for a number of higher dimensional polytopes with E < sub > 8 </ sub > symmetry, shown in orthogonal projections in the E < sub > 8 </ sub > Coxeter plane:
The Institute is also responsible for the Petrie Museum of Egyptian Archaeology which is open to the public on a regular basis.
Petrie railway station provides access to regular Citytrain services to Brisbane and Ipswich, as well as Caboolture and the Sunshine Coast.

regular and polygon
They are distinct from the Platonic solids, which are composed of only one type of polygon meeting in identical vertices, and from the Johnson solids, whose regular polygonal faces do not meet in identical vertices.
For example, the perimeter of a regular polygon inscribed in a circle approaches the circumference with increasing numbers of sides ( and decrease in the length of one side ).
While at university, Gauss independently rediscovered several important theorems ; his breakthrough occurred in 1796 when he showed that any regular polygon with a number of sides which is a Fermat prime ( and, consequently, those polygons with any number of sides which is the product of distinct Fermat primes and a power of 2 ) can be constructed by compass and straightedge.
The wheels can be any regular polygon except a triangle, but the catenary must have parameters corresponding to the shape and dimensions of the wheels.
For example, every polygon is topologically self-dual ( it has the same number of vertices as edges, and these are switched by duality ), but will not in general be geometrically self-dual ( up to rigid motion, for instance ) – regular polygons are geometrically self-dual ( all angles are congruent, as are all edges, so under duality these congruences swap ), but irregular polygons may not be geometrically self-dual.
In geometry, a Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform, i. e., not a Platonic solid, Archimedean solid, prism or antiprism.
Since a regular polygon has angles at least 60 degrees, it follows that at most five faces meet at any vertex.
Although there is no obvious restriction that any given regular polygon cannot be a face of a Johnson solid, it turns out that the faces of Johnson solids always have 3, 4, 5, 6, 8, or 10 sides.
* Star polygon: a polygon which self-intersects in a regular way.
* Regular: A polygon is regular if it is both cyclic and equilateral.
A non-convex regular polygon is called a regular star polygon.
Any polygon, regular or irregular, self-intersecting or simple, has as many corners as it has sides.
The area of a regular polygon is also given in terms of the radius r of its inscribed circle and its perimeter p by
While it is possible to construct analogies to the Penrose triangle with other regular polygons to create a Penrose polygon, the visual effect is not as striking, and as the sides increase, the object seems merely to be warped or twisted.
Carl Friedrich Gauss in 1796 showed that a regular n-sided polygon can be constructed with ruler and compass if the odd prime factors of n are distinct Fermat primes.
Some regular polygons, like the heptagon, become constructible ; and John H. Conway gives constructions for several of them ; but the 11-sided polygon, the hendecagon, is still impossible, and infinitely many others.
* a regular polygon that can be constructed with compass and straightedge ; see constructible polygon.
In mathematics, a dihedral group is the group of symmetries of a regular polygon, including both rotations and reflections.
In this article, D < sub > n </ sub > ( and sometimes Dih < sub > n </ sub >) refers to the symmetries of a regular polygon with n sides.

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