The Mathematical Monthly, Volume 21860 |
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Page 76
... polygon of n sides , each side being equal to 2r , twice the required radius . Join the centre of the polygon with the centre of 76 -
... polygon of n sides , each side being equal to 2r , twice the required radius . Join the centre of the polygon with the centre of 76 -
Page 77
Join the centre of the polygon with the centre of each circle . In each of the n equal triangles thus formed , the angle at the centre of the polygon is one nth of four right angles , or 2π n 2 π n ; and the sum of ( n 2 ) π = the n the ...
Join the centre of the polygon with the centre of each circle . In each of the n equal triangles thus formed , the angle at the centre of the polygon is one nth of four right angles , or 2π n 2 π n ; and the sum of ( n 2 ) π = the n the ...
Page 305
... polygons or rectilinear plane figures with a given number of sides and a given perimeter , that figure contains the ... polygon which has the greatest number of sides , so that among plane figures the circle has the greatest area for a ...
... polygons or rectilinear plane figures with a given number of sides and a given perimeter , that figure contains the ... polygon which has the greatest number of sides , so that among plane figures the circle has the greatest area for a ...
Page 320
... polygon is less than a circle isoperimetrical with it , and that any other polygon is less than a regular one , isoperimetrical with it . 116. Let us begin , however , by defining a few of the words we shall need to use . 117. A polygon ...
... polygon is less than a circle isoperimetrical with it , and that any other polygon is less than a regular one , isoperimetrical with it . 116. Let us begin , however , by defining a few of the words we shall need to use . 117. A polygon ...
Page 321
... polygon . 131. If a polygon , about which a circle can be circumscribed , or in which a circle can be in- scribed , has its sides equal , one to the other , the polygon is called a regular polygon , and the centre of these circles is ...
... polygon . 131. If a polygon , about which a circle can be circumscribed , or in which a circle can be in- scribed , has its sides equal , one to the other , the polygon is called a regular polygon , and the centre of these circles is ...
Common terms and phrases
a₁ astronomers atmosphere axis b₁ body cells centre CHARLES HENRY DAVIS circle coefficients College computation conic section constant cos² curve denote distance divided earth's ellipse equal equation force fraction Geometry given gives Hamilton College hence hyperbola inscribed integral logarithms Marietta College Mass Mathematical Monthly maximum Mercury motion multiplied observations obtain parallel perihelion perpendicular Perry City plane polygon Prize is awarded PRIZE PROBLEMS PRIZE SOLUTION Probs Prof Prop proposition quantities quaternions quotient R₁ radius ratio regular polygon remainder result rhombs right angles roots rotation sides SIMON NEWCOMB sin² sine SOLUTION OF PROBLEM sphere spherical square supposed surface tangent Theorem tion triangle TRUMAN HENRY SAFFORD vector velocity whole number
Popular passages
Page 113 - Multiplying or dividing both terms of a fraction by the same number does not change its value.
Page 60 - Method of correcting the apparent distance of the Moon from the Sun, or a Star, for the effects of Parallax and Refraction.
Page 224 - Physical Optics, Part II. The Corpuscular Theory of Light discussed Mathematically. By RICHARD POTTER, MA Late Fellow of Queens' College, Cambridge, Professor of Natural Philosophy and Astronomy in University College, London.
Page 326 - PUCKLE.— An Elementary Treatise on Conic Sections and Algebraic Geometry. With a numerous collection of Easy Examples progressively arranged, especially designed for the use of Schools and Beginners. By G. HALE PUCKLE, MA, Principal of Windermere College.
Page 285 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 305 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 326 - AN ELEMENTARY TREATISE ON THE LUNAR THEORY, with a Brief Sketch of the Problem up to the time of Newton. Second Edition, revised. Crown 8vo. cloth. 5*. 6d. Hemming. — AN ELEMENTARY TREATISE ON THE DIFFERENTIAL AND INTEGRAL CALCULUS, for the Use; of Colleges and Schools.
Page 360 - URIAH A. BOYDEN, ESQ., of Boston, Mass., has deposited with THE FRANKLIN INSTITUTE the sum of one thousand dollars, to be awarded as a premium to "Any resident of North America who shall determine by experiment whether all rays of light,* and other physical rays, are or are not transmitted with the same velocity.
Page 358 - Calculus — a connection which in some instances involves far more than a merely formal analogy. The work is in some measure designed as a sequel to Professor Boole's Treatise on Differential Equations.
Page 321 - First, that the maximum of polygons formed of given sides may be inscribed in a circle ; secondly, that the maximum of isoperimetrical polygons having a given number of sides has its sides equal ; and thirdly, that such a regular polygon is of smaller area than a circle isoperimetrical with it. 134. Theorem. The area of a triangle is found by multiplying the base by half the altitude. This theorem has been already proved (Art. 111). 135. We shall need the Pythagorean proposition, which implies all...