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Line-bound vectors, plane-bound bivectors and tetrahedra in the conformal model of three-dimensional space. (English) Zbl 1541.15029

Silva, David W. (ed.) et al., Advanced computational applications of geometric algebra. First international conference, ICACGA 2022, Denver, CO, USA, October 2–5, 2022. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 13771, 27-39 (2024).

MSC: 15A67 51M04 51M15

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Havel, Timothy F.

Heron’s formula in higher dimensions. (English) Zbl 1534.51012

Adv. Appl. Clifford Algebr. 34, No. 2, Paper No. 9, 30 p. (2024).

MSC: 51M04 11E88 15A67 51M25 51M30 52A38 52B11

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Havel, Timothy F.

An extension of Heron’s formula to tetrahedra, and the projective nature of its zeroes. I. (English) Zbl 1535.51016

Pi Mu Epsilon J. 15, No. 9, 539-551 (2023).

MSC: 51M04 51M25 51M16

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Donovan, Peter

Heron’s formula and the 3-dimensional Pythagoras theorem. (English) Zbl 1535.51015

Aust. Math. Soc. Gaz. 50, No. 1, 22-23 (2023).

Reviewer: Antoine Mhanna (Kfardebian)

MSC: 51M04

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Klain, Daniel A.

Tetrahedra with congruent facet pairs. (English) Zbl 1537.51013

Math. Intell. 45, No. 3, 251-255 (2023).

Reviewer: M. G. Mahmoudi (Tehran)

MSC: 51M04

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Vandervelde, Sam

Conway’s dream. (English) Zbl 1525.51012

Math. Intell. 45, No. 1, 19-21 (2023).

Reviewer: Lienhard Wimmer (Isny)

MSC: 51M04

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Kock, Anders

Heron’s formula, and volume forms. (English) Zbl 1509.51003

Cah. Topol. Géom. Différ. Catég. 63, No. 3, 239-258 (2022).

Reviewer: Hirokazu Nishimura (Tsukuba)

MSC: 51K10 51M25

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Lévy-Leblond, Jean-Marc

A symmetric 3D proof of Heron’s formula. (English) Zbl 1493.51007

Math. Intell. 43, No. 2, 37-39 (2021).

Reviewer: Martin Lukarevski (Skopje)

MSC: 51M04 51M25

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Sarkar, Jyotirmoy

The smallest ellipse that covers two circles. (English) Zbl 1536.51018

Math. Stud. 89, No. 3-4, 67-89 (2020).

MSC: 51N20 51M04

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Khimshiashvili, Giorgi

Symmetric foliations in spaces of triangles. (English) Zbl 1516.53030

Rep. Enlarged Sess. Semin. I. Vekua Inst. Appl. Math. 34, 50-53 (2020).

MSC: 53C12 57R30

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László, Lajos

An inequality for the powers of triangle sides. (English) Zbl 1474.51019

Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput. 50, 219-229 (2020).

MSC: 51M16 51M25 51M04

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Çolakoğlu, Harun Barış

Area of a triangle in terms of the \(m\)-generalized taxicab distance. (English) Zbl 1438.51002

Konuralp J. Math. 7, No. 1, 222-227 (2019).

MSC: 51K05 51K99 51N20

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Levrie, Paul

A straightforward proof of Descartes’s circle theorem. (English) Zbl 1428.51009

Math. Intell. 41, No. 3, 24-27 (2019).

Reviewer: Martin Lukarevski (Skopje)

MSC: 51M04 51M15 51M25

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Abrosimov, Nikolay; Mednykh, Alexander

Area and volume in non-Euclidean geometry. (English) Zbl 1416.51020

Alberge, Vincent (ed.) et al., Eighteen essays in non-Euclidean geometry. Zürich: European Mathematical Society (EMS). IRMA Lect. Math. Theor. Phys. 29, 151-189 (2019).

MSC: 51M25 51M10

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Kudina, Ekaterina S.; Mednykh, Alexander D.

On the asymptotics of volume for non-Euclidean simplices. (English. Russian original) Zbl 1431.51012

Russ. Math. Surv. 72, No. 5, 974-976 (2017); translation from Usp. Mat. Nauk 72, No. 5, 195-196 (2017).

MSC: 51M25 51M10 51M20

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Dobbs, David E.

On triangles with the same area. (English) Zbl 1384.51007

Far East J. Math. Educ. 17, No. 1, 1-23 (2017).

MSC: 51M04

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Hajja, Mowaffaq; ShahAli, Hassan Ali

Simpler proofs of Jian Liu’s inequalities. (English) Zbl 1377.51012

J. Geom. 108, No. 2, 565-574 (2017).

MSC: 51M16 51N20

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Izadi, Farzali; Khoshnam, Foad; Shamsi Zargar, Arman

Rank of elliptic curves associated to Brahmagupta quadrilaterals. (English) Zbl 1365.11069

Colloq. Math. 143, No. 2, 187-192 (2016).

MSC: 11G05 14H52

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Carter, J. Scott; Mullens, David A.

Some elementary aspects of 4-dimensional geometry. (English) Zbl 1379.51007

Symmetry 7, No. 2, 515-545 (2015).

Reviewer: Sándor Nagydobai Kiss (Satu Mare)

MSC: 51M25 51M04

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Izadi, Farzali; Nabardi, Kamran

A family of elliptic curves with rank \(\geq 5\). (English) Zbl 1374.11068

Period. Math. Hung. 71, No. 2, 243-249 (2015).

Reviewer: Günter Lettl (Graz)

MSC: 11G05 14H52

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Gelişgen, Ö.; Ermiş, T.

Area formulas for a triangle in the \(m\)-plane. (English) Zbl 1366.51009

Konuralp J. Math. 2, No. 2, 85-95 (2014).

MSC: 51M25

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Taisbak, Christian Marinus

An Archimedean proof of Heron’s formula for the area of a triangle: heuristics reconstructed. (English) Zbl 1283.01010

Sidoli, Nathan (ed.) et al., From Alexandria, through Baghdad. Surveys and studies in the ancient Greek and medieval Islamic mathematical sciences in honor of J. L. Berggren. Berlin: Springer (ISBN 978-3-642-36735-9/hbk; 978-3-642-36736-6/ebook). 189-198 (2014).

Reviewer: Victor V. Pambuccian (Phoenix)

MSC: 01A20 51-03 51M25

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González Llorente, José

Extraordinary architectures, heroes, billiards and problems of maxima and minima. (Spanish) Zbl 1301.51025

Gac. R. Soc. Mat. Esp. 16, No. 2, 241-269 (2013).

Reviewer: Robert W. van der Waall (Huizen)

MSC: 51M16 00A66 01A20 52A40 01A85 01A60 51-03

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Çolakoğlu, Harun Bariş; Gelişgen, Özcan; Kaya, Rüstem

Area formulas for a triangle in the alpha plane. (English) Zbl 1281.51012

Math. Commun. 18, No. 1, 123-132 (2013).

Reviewer: Erich W. Ellers (Toronto)

MSC: 51K05 51K99

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Mednykh, A. D.

Brahmagupta formula for cyclic quadrilaterials in the hyperbolic plane. (English) Zbl 1330.51009

Sib. Èlektron. Mat. Izv. 9, 247-255 (2012).

MSC: 51M09

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Nishiyama, Yutaka

Measuring areas: from polygons to land maps. (English) Zbl 1259.28003

Int. J. Pure Appl. Math. 81, No. 1, 91-100 (2012).

MSC: 28-01 00A09 97M50 97G99 97I50

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Hess, Albrecht

A highway from Heron to Brahmagupta. (English) Zbl 1244.51005

Forum Geom. 12, 191-192 (2012).

MSC: 51M04 51M15

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Ostermann, Alexander; Wanner, Gerhard

Geometry by its history. (English) Zbl 1288.51001

Undergraduate Texts in Mathematics. Readings in Mathematics. Berlin: Springer (ISBN 978-3-642-29162-3/hbk; 978-3-642-29163-0/ebook). xii, 437 p. (2012).

Reviewer: Mowaffaq Hajja (Irbid)

MSC: 51-01 51-03 01A05 51M04 51M05 51M15 51N10 51N15