"बहुभुज": अवतरणों में अंतर
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Manojkumar.a (वार्ता | योगदान) नया पृष्ठ: बहुभुज एक त्रिकोणमितीय आकृति है जो समतल सतह पर बना होता है. बहुभु... |
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पंक्ति 1:
'''बहुभुज''' एक त्रिकोणमितीय आकृति है जो [[समतल]] सतह पर बना होता है. बहुभुज कई [[सरल
बहुभुज अंग्रेजी शब्द पोलीगोन का हिंदी रूपांतरण है. अंग्रेजी में पोलीगोन शब्द ग्रीक भाषा के दो शब्दों को मिलने से बना है. इसमें पहला शब्द पोली यानी बहुत और गोनिया यानी कोण. इस तरह पोलीगोन का अर्थ [[बहुकोण]] है. इसी तरह बहुभुज [[संस्कृत]] के दो शब्दो के मेल से बनाया गया है. जिसमें बहु यानी अनेक और भुज यानी भुजा अर्थ देता है. हिंदी में अंग्रेजी के कोण की जगह भुजा को स्वीकार किया गया है. और इस तरह बहुभुज का जन्म हुआ है.
आमतौर पर दो सरल रेखाओं के मिलने से कोण बनता है. लेकिन इसका मान 180 डिग्री नहीं होता है, क्योंकि ऐसा होने से ये कोण [[सरल रेखा]] बन जाएगा.
==बहुभुज का नामकरण==
बहुभुज का अर्थ अनेक भुजाओं वाली आकृति। वैसी आकृति जिसमें जो तीन या तीन से अधिक रेखाओं से मिलकर बनी हो बहुभुज कहलाती है. भुज में संस्कृत मूल से बने गिनती के उपसर्गों को जोड़कर बहुभुज का नामकरण किया जाता है. बहुभुज में भुजाओं की संख्या के आधार पर उनका नामकरण किया जाता है. combining a Greek-derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle, quadrilateral or quadrangle, and nonagon are exceptions. For large numbers, mathematicians usually write the numeral itself, e.g. 17-gon. A variable can even be used, usually n-gon. This is useful if the number of sides is used in a formula.
Some special polygons also have their own names; for example the regular star pentagon is also known as the pentagram.
Polygon names Name Edges Remarks
henagon (or monogon) 1 In the Euclidean plane, degenerates to a closed curve with a single vertex point on it.
digon 2 In the Euclidean plane, degenerates to a closed curve with two vertex points on it.
triangle (or trigon) 3 The simplest polygon which can exist in the Euclidean plane.
quadrilateral (or quadrangle or tetragon) 4 The simplest polygon which can cross itself.
pentagon 5 The simplest polygon which can exist as a regular star. A star pentagon is known as a pentagram or pentacle.
hexagon 6
heptagon 7 avoid "septagon" = Latin [sept-] + Greek
octagon 8
enneagon (or nonagon) 9
decagon 10
hendecagon 11 avoid "undecagon" = Latin [un-] + Greek
dodecagon 12 avoid "duodecagon" = Latin [duo-] + Greek
tridecagon (or triskaidecagon) 13
tetradecagon (or tetrakaidecagon) 14
pentadecagon (or quindecagon or pentakaidecagon) 15
hexadecagon (or hexakaidecagon) 16
heptadecagon (or heptakaidecagon) 17
octadecagon (or octakaidecagon) 18
enneadecagon (or enneakaidecagon or nonadecagon) 19
icosagon 20
No established English name 100 "hectogon" is the Greek name (see hectometre), "centagon" is a Latin-Greek hybrid; neither is widely attested.
chiliagon 1000 Pronounced /ˈkɪliəɡɒn/), this polygon has 1000 sides. The measure of each angle in a regular chiliagon is 179.64°.
René Descartes used the chiliagon and myriagon (see below) as examples in his Sixth meditation to demonstrate a distinction which he made between pure intellection and imagination. He cannot imagine all thousand sides [of the chiliagon], as he can for a triangle. However, he clearly understands what a chiliagon is, just as he understands what a triangle is, and he is able to distinguish it from a myriagon. Thus, he claims, the intellect is not dependent on imagination.[3]
myriagon 10,000 See remarks on the chiliagon.
megagon [4] 1,000,000 The internal angle of a regular megagon is 179.99964 degrees.
To construct the name of a polygon with more than 20 and less than 100 edges, combine the prefixes as follows
Tens and Ones final suffix
-kai- 1 -hena- -gon
20 icosi- 2 -di-
30 triaconta- 3 -tri-
40 tetraconta- 4 -tetra-
50 pentaconta- 5 -penta-
60 hexaconta- 6 -hexa-
70 heptaconta- 7 -hepta-
80 octaconta- 8 -octa-
90 enneaconta- 9 -ennea-
The "kai" is not always used. Opinions differ on exactly when it should, or need not, be used (see also examples above).
That is, a 42-sided figure would be named as follows:
Tens and Ones final suffix full polygon name
tetraconta- -kai- -di- -gon tetracontakaidigon
and a 50-sided figure
Tens and Ones final suffix full polygon name
pentaconta- -gon pentacontagon
But beyond enneagons and decagons, professional mathematicians generally prefer the aforementioned numeral notation (for example, MathWorld has articles on 17-gons and 257-gons). Exceptions exist for side numbers that are difficult to express in numerical form.
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