Talk:Rhombus

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Semi-protected edit request on 27 November 2019 : Missing expression of rhombus inradius
Hi!

Please add the missing expression of the rhombus inradius: $$ r = {{(\sin \alpha) \cdot a} \over 2} $$ ; it is featured in Eric Weisstein's Rhombus page, in Wolfram Mathworld (page already referenced in the Wikipedia Rhombus article), where it is derived from the other expression of the rhombus inradius: $$ r = {{p \cdot q} \over {2\sqrt{p^2+q^2}}} $$ (other expression already featured in the Wikipedia Rhombus article).

Thank you in advance!

(my wikipedian anonymous pseudonym)

€;-)

- 2A01:CB00:8697:8100:C047:A0C9:E3E4:74FC (talk) 17:01, 27 November 2019 (UTC)


 * ✅ –Deacon Vorbis (carbon &bull; videos) 19:22, 27 November 2019 (UTC)
 * Great! Thank you for being so quick! Uh... and, by any chance, from a pedagogical point of view, what about adding the other vertex angle expression: $$ r = {{a \sin \alpha} \over 2} = {{a \sin \beta} \over 2} $$ ?
 * €:-P
 * - 2A01:CB00:8697:8100:E82C:4B76:1E81:EDBA (talk) 22:00, 27 November 2019 (UTC)
 * Um... or, maybe... why not adding the associate expression of r in terms of the rhombus height h :
 * $$ r = {{a \sin \alpha} \over 2} = {h \over 2} $$ ?
 * €:-P
 * - 2A01:CB00:8697:8100:ADB9:8585:130F:A819 (talk) 22:12, 28 November 2019 (UTC)
 * Er... well, perhaps... what about adding a little note, something like:
 * Note: r can also be expressed in terms of the rhombus height h :
 * $$ r = {h \over 2} $$ ?
 * €:-P
 * (This relation is not so obvious, because strictly speaking, a height lies on a vertex, and does not lie on the center of the inscribed circle of a rhombus.)
 * - 2A01:CB00:8697:8100:ADB9:8585:130F:A819 (talk) 14:27, 29 November 2019 (UTC)
 * Oops! I forgot to provide the parameters of a web site providing the expression of the rhombus height h in terms of the rhombus side a and any vertex angle:
 * $$(~h = a \sin \alpha = a \sin \beta~)$$ :
 * Furey, Edward. "Rhombus Calculator"; CalculatorSoup, https://www.calculatorsoup.com - Online Calculators
 * - 2A01:CB00:8697:8100:B1A2:BF28:42A4:3C20 (talk) 20:51, 29 November 2019 (UTC)
 * - 2A01:CB00:8697:8100:ADB9:8585:130F:A819 (talk) 00:07, 30 November 2019 (UTC)
 * Er... well, perhaps... what about adding a little note, something like:
 * Note: r can also be expressed in terms of the rhombus height h :
 * $$ r = {h \over 2} $$ ?
 * €:-P
 * (This relation is not so obvious, because strictly speaking, a height lies on a vertex, and does not lie on the center of the inscribed circle of a rhombus.)
 * - 2A01:CB00:8697:8100:ADB9:8585:130F:A819 (talk) 14:27, 29 November 2019 (UTC)
 * Oops! I forgot to provide the parameters of a web site providing the expression of the rhombus height h in terms of the rhombus side a and any vertex angle:
 * $$(~h = a \sin \alpha = a \sin \beta~)$$ :
 * Furey, Edward. "Rhombus Calculator"; CalculatorSoup, https://www.calculatorsoup.com - Online Calculators
 * - 2A01:CB00:8697:8100:B1A2:BF28:42A4:3C20 (talk) 20:51, 29 November 2019 (UTC)
 * - 2A01:CB00:8697:8100:ADB9:8585:130F:A819 (talk) 00:07, 30 November 2019 (UTC)
 * - 2A01:CB00:8697:8100:ADB9:8585:130F:A819 (talk) 14:27, 29 November 2019 (UTC)
 * Oops! I forgot to provide the parameters of a web site providing the expression of the rhombus height h in terms of the rhombus side a and any vertex angle:
 * $$(~h = a \sin \alpha = a \sin \beta~)$$ :
 * Furey, Edward. "Rhombus Calculator"; CalculatorSoup, https://www.calculatorsoup.com - Online Calculators
 * - 2A01:CB00:8697:8100:B1A2:BF28:42A4:3C20 (talk) 20:51, 29 November 2019 (UTC)
 * - 2A01:CB00:8697:8100:ADB9:8585:130F:A819 (talk) 00:07, 30 November 2019 (UTC)
 * Furey, Edward. "Rhombus Calculator"; CalculatorSoup, https://www.calculatorsoup.com - Online Calculators
 * - 2A01:CB00:8697:8100:B1A2:BF28:42A4:3C20 (talk) 20:51, 29 November 2019 (UTC)
 * - 2A01:CB00:8697:8100:ADB9:8585:130F:A819 (talk) 00:07, 30 November 2019 (UTC)
 * - 2A01:CB00:8697:8100:B1A2:BF28:42A4:3C20 (talk) 20:51, 29 November 2019 (UTC)
 * - 2A01:CB00:8697:8100:ADB9:8585:130F:A819 (talk) 00:07, 30 November 2019 (UTC)
 * - 2A01:CB00:8697:8100:B1A2:BF28:42A4:3C20 (talk) 20:51, 29 November 2019 (UTC)
 * - 2A01:CB00:8697:8100:ADB9:8585:130F:A819 (talk) 00:07, 30 November 2019 (UTC)
 * - 2A01:CB00:8697:8100:ADB9:8585:130F:A819 (talk) 00:07, 30 November 2019 (UTC)

Rhombus height expression missing, although h used in area formulas.
Hi!

My last edit request section seems to be deactivated...

Please add the missing expression of the rhombus height h in terms of the rhombus side a and any vertex angle:

$$ h = a \sin \alpha = a \sin \beta $$ ;

it can be sourced by the following website, where it is featured:

Furey, Edward. "Rhombus Calculator"; CalculatorSoup, https://www.calculatorsoup.com - Online Calculators.

Then, please add the missing expression of the rhombus height h in terms of the rhombus inradius r :

$$ h = 2r $$ ; or: $$ r = {h \over 2} $$ ;

it is just mentioned in the little caption under a figure of the article:

"The height h is the perpendicular distance between any two non-adjacent sides, which equals the diameter of the circle inscribed."

Double thank you in advance!

€:-) €:-)

(my Wikipedia anonymous pseudonym)

€;-)

- 2A01:CB00:8697:8100:3531:F012:5113:D6E5 (talk) 20:22, 1 December 2019 (UTC) "Alert":

the rhombus article uses the rhombus height h in 2 different area formulas:

$$ K = a \cdot h $$, and:

$$ K = \frac {h^2}{\sin \alpha} $$ ,

without providing an expression of h ,

and without noting that h is unique;

this is not "mathematically correct"...

€:-P

- 2A01:CB00:8697:8100:F964:F02D:1FD7:636C (talk) 19:27, 2 December 2019 (UTC)

Rhombic icosahedron: Two types of rhombi?
This WP "Rhombus" article features a table classifying "Rhombic icosahedron" as having "Two types of rhombi";

the WP "Rhombic icosahedron" article says:

"A rhombic icosahedron [...] has 10 faces on the axis of symmetry with 10 rhombi following the equator. [...] all the faces are congruent [...]."

Something must be clarified, somewhere...!

RavBol (talk) 22:33, 18 December 2019 (UTC)

Use of term "diamond"
Is there a source for the notion that the word "diamond" is sometimes used specifically for the rhombus that has a 60° angle, rather than as a synonym for "rhombus"? In any case, not all diamonds on playing cards do have this angle. And the rhombus with a 60° angle is not exactly a "projection" of adjacent faces of an octahedron. Rather it is the 2D figure you get if you rotate one of the faces about their shared edge until it is coplanar with the other face. It is a part of a 2D net of an octahedron. So the opening paragraph needs some amendment. Vumbin (talk) 22:17, 27 October 2021 (UTC)
 * I agree with Vumbin that the reference to octahedral projections is not correct. Also, playing card diamonds do not generally have 60° angles. On the other hand, I think the reference to "diamonds" having 60° angles is from the usage as a polyiamond, where it does have to be 60°. This opening paragraph needs editing. --seberle (talk) 22:08, 20 November 2021 (UTC)