Simple Constructions for the Regular Pentagon and Heptadecagon

1989 ◽  
Vol 82 (5) ◽  
pp. 361-365
Author(s):  
Duane W. Detemple
Keyword(s):  
Pythagorean Theorem ◽  
Regular Polygons ◽  
Common Elements ◽  
Regular Pentagon ◽  
Interesting Variation ◽  
Construction Works ◽  
Distance Formula

This article discusses two new Euclidean constructions to inscribe regular polygons of five and seventeen sides in a circle. The pentagon's construction shares many common elements with the familiar Ptolemaic method (see, e.g., Jacobs [1982, 254 55]), but an interesting variation occurs in the final steps. The explanation given for why the construction works is unusual in that it does not make use of the distance formula of the Pythagorean theorem.

A ousadia do π ser racional

2020 ◽  
Author(s):  
Sidney Silva
Keyword(s):  
Rational Number ◽  
Pythagorean Theorem ◽  
Regular Polygons ◽  
The Real ◽  
Mathematical Question ◽  
Lower Limits ◽  
Mathematical Constant ◽  
Real Area

Pi (π) is used to represent the most known mathematical constant. By definition, π is the ratio of the circumference of a circle to its diameter. In other words, π is equal to the circumference divided by the diameter (π = c / d). Conversely, the circumference is equal to π times the diameter (c = π . d). No matter how big or small a circle is, pi will always be the same number. The first calculation of π was made by Archimedes of Syracuse (287-212 BC) who approached the area of a circle using the Pythagorean Theorem to find the areas of two regular polygons: the polygon inscribed within the circle and the polygon within which circle was circumscribed. Since the real area of the circle is between the areas of the inscribed and circumscribed polygons, the polygon areas gave the upper and lower limits to the area of the circle. Archimedes knew he had not found the exact value of π, but only an approximation within these limits. In this way, Archimedes showed that π is between 3 1/7 (223/71) and 3 10/71 (22/7). This research demonstrates that the value of π is 3.15 and can be represented by a fraction of integers, a/b, being therefore a Rational Number. It also demonstrates by means of an exercise that π = 3.15 is exact in 100% in the mathematical question.

Mathematical Lens: How Much Can You Bench?

2013 ◽  
Vol 106 (6) ◽  
pp. 414-417
Author(s):  
Chris A. Bolognese
Keyword(s):  
Pythagorean Theorem ◽  
Regular Polygons ◽  
Scale Factors

Students analyze a photograph to solve mathematical questions related to the images captured in the photograph. This month the mathematics behind the photograph includes finding areas of regular polygons, right triangle trigonometry, the Pythagorean theorem, special right triangles, and similarity and scale factors.

Generalized Second Moment of Areas of Regular Polygons for Ludwick Type Material and its Application to Cantilever Column Buckling

2019 ◽  
Vol 19 (02) ◽  
pp. 1950010
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Cross Sections ◽  
Equilateral Triangle ◽  
Regular Polygon ◽  
Regular Hexagon ◽  
Type Material ◽  
Regular Polygons ◽  
Column Buckling ◽  
Second Moment ◽  
Regular Pentagon

This study deals with the generalized second moment of area (GSMA) of regular polygon cross-sections for the Ludwick type material and its application to cantilever column buckling. In the literature, the GSMA for the Ludwick type material has only been considered for rectangular, elliptical and superellipsoidal cross-sections. This study calculates the GSMAs of regular polygon cross-sections other than those mentioned above. The GSMAs calculated by varying the mechanical constant of the Ludwick type material for the equilateral triangle, square, regular pentagon, regular hexagon and circular cross-sections are reported in tables and figures. The GSMAs obtained from this study are applied to cantilever column buckling, with results shown in tables and figures.

scholarly journals The chord length distribution function for regular polygons

2009 ◽  
Vol 41 (2) ◽  
pp. 358-366 ◽  
Author(s):  
H. S. Harutyunyan ◽  
V. K. Ohanyan
Keyword(s):  
Distribution Function ◽  
Regular Polygon ◽  
Length Distribution ◽  
Chord Length ◽  
Regular Hexagon ◽  
Regular Polygons ◽  
Chord Length Distribution ◽  
Regular Pentagon ◽  
Regular Triangle ◽  
Elementary Expression

In this paper we obtain an elementary expression for the chord length distribution function of a regular polygon. The formula is derived using δ-formalism in Pleijel identity. In the particular cases of a regular triangle, a square, a regular pentagon, and a regular hexagon, our formula coincides with the results of Sulanke (1961), Gille (1988), Aharonyan and Ohanyan (2005), and Harutyunyan (2007), respectively.

scholarly journals The chord length distribution function for regular polygons

2009 ◽  
Vol 41 (02) ◽  
pp. 358-366
Author(s):  
H. S. Harutyunyan ◽  
V. K. Ohanyan
Keyword(s):  
Distribution Function ◽  
Regular Polygon ◽  
Length Distribution ◽  
Chord Length ◽  
Regular Hexagon ◽  
Regular Polygons ◽  
Chord Length Distribution ◽  
Regular Pentagon ◽  
Regular Triangle ◽  
Elementary Expression

In this paper we obtain an elementary expression for the chord length distribution function of a regular polygon. The formula is derived using δ-formalism in Pleijel identity. In the particular cases of a regular triangle, a square, a regular pentagon, and a regular hexagon, our formula coincides with the results of Sulanke (1961), Gille (1988), Aharonyan and Ohanyan (2005), and Harutyunyan (2007), respectively.

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