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Triongl hafalochrog

Triongl hafalochrog, lle mae'r:
* ochrau'n hafal (a=b=c),
* yr onglau'n hafal (),
* yr uchderau'n hafal (ha=hb=hc).

Mewn geometreg, polygon rheolaidd yw'r triongl hafalochrog, sy'n driongl lle mae'r dair ochr yn gyfartal. O fewn geometreg Ewclidaidd, mae gan pob triongl hafalochrog ochrau cyfath, sy'n 60 ° yr un.

Prif nodweddion

[golygu | golygu cod]

O ddynodi hyd yr ochrau yn a, yna fe ellir dweud, gan ddefnyddio Theorem Pythagoras fod:

  1. yr arwynebedd yn
  2. y perimedr yn
  3. radiws yr amgylch (circumscribed circle) yn
  4. radiws y mewngylch (inscribed circle) yn neu
  5. canol geometrig y triongl hefyd yn ganol i'r amgylch a'r mewnglych
  6. uchder (neu hyd) o bob ochr yn .

O ddynodi radiws yr amgylch yn R, yna fe eelir dweud, drwy ddefnyddio trigonometreg fod:

  • yr arwynebedd yn [1]

Ceir perthynas syml rhwng yr llawer o'r meintiau hyn ag uchder ("h") pob fertig o'r ochr gyferbyn:

  1. Yr arwynebedd yw
  2. Uchder y canol o bob ochr (hy yr apothem), yw
  3. Radiws y cylch sy'n amgylchu'r 3 fertig yw
  4. Radiws y mewngylch yw


Polygonau

Triongl | Pedrochr | Pentagon | Hecsagon | Heptagon | Octagon | Nonagon | Decagon | Hendecagon | Dodecagon | Triskaidecagon | Tetradecagon | Pentadecagon | Hexadecagon | Heptadecagon | Octadecagon | Enneadecagon | Icosagon | Chiliagon | Myriagon


Cyfeiriadau

[golygu | golygu cod]
  1. Bencze, Mihály; Wu, Hui-Hua; Wu, Shan-He (2008). "An equivalent form of fundamental triangle inequality and its applications". Research Group in Mathematical Inequalities and Applications 11 (1). http://rgmia.org/papers/v11n1/equivalent.pdf.
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Triongl hafalochrog
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