Teng yonli uchburchak
Qiyofa
Geometriyada teng yonli uchburchak — tomonlaridan ikkitasi teng boʻlgan uchburchak. Teng tomonlari qarshisidagi burchaklari ham oʻzaro teng. Teng yonli uchburchaklarga teng yonli toʻgʻri burchakli uchburchak, oltin uchburchak va dipiramidalarni misol oʻlaroq koʻrsatish mumkin.
Teng yonli uchburchaklarni matematik oʻrganish qadimgi Misr matematikasi va Bobil matematikasiga borib taqaladi. Teng yonli uchburchaklar qadim zamonlardan buyon dekoratsiya oʻlaroq foydalanilgan hamda koʻpincha arxitektura va dizaynda, masalan, binolar frontonlarida paydo boʻlgandir.
Formulalar
[tahrir | manbasini tahrirlash]- Balandligini topish formulasi: .
- Perimetrini topish formulasi: .
Ichki chizilgan aylana radiusini topish formulalari:
Yana qarang
[tahrir | manbasini tahrirlash]Manbalar
[tahrir | manbasini tahrirlash]- Alsina, Claudi; Nelsen, Roger B. (2009), When less is more: Visualizing basic inequalities, The Dolciani Mathematical Expositions, 36-jild, Mathematical Association of America, Washington, DC, ISBN 978-0-88385-342-9, MR 2498836
- Arslanagić, Šefket, „Problem η44“, Inequalities proposed in Crux Mathematicorum (PDF), 151-bet
- Ball, W. W. Rouse; Coxeter, H. S. M. (1987) [1892], Mathematical Recreations and Essays (13th-nashr), Dover, footnote, p. 77, ISBN 0-486-25357-0
- Baloglou, George; Helfgott, Michel (2008), „Angles, area, and perimeter caught in a cubic“ (PDF), Forum Geometricorum, 8: 13–25, MR 2373294, 2022-06-23da asl nusxadan (PDF) arxivlandi, qaraldi: 2021-09-30
- Bardell, Nicholas S. (2016), „Cubic polynomials with real or complex coefficients: The full picture“ (PDF), Australian Senior Mathematics Journal, 30 (2): 5–26
- Barnes, John (2012), Gems of Geometry (2nd, illustrated-nashr), Springer, 27-bet, ISBN 9783642309649
- Bezdek, András; Bisztriczky, Ted (2015), „Finding equal-diameter triangulations in polygons“, Beiträge zur Algebra und Geometrie, 56 (2): 541–549, doi:10.1007/s13366-014-0206-6, MR 3391189
- Bolton, Nicholas J; Nicol, D.; Macleod, G. (March 1977), „The geometry of the Śrī-yantra“, Religion, 7 (1): 66–85, doi:10.1016/0048-721x(77)90008-2
- Clagett, Marshall (1989), Ancient Egyptian Science: Ancient Egyptian mathematics, American Philosophical Society, Footnote 68, pp. 195–197, ISBN 9780871692320
{{citation}}
: Andozada hech qanday qiymat berilmagan (boʻsh) nomaʼlum parametr mavjud:|1=
(yordam) - Conway, J.H.; Guy, R.K. (1996), „Calabi's Triangle“, The Book of Numbers, New York: Springer-Verlag, 206-bet
- Conway, John; Ryba, Alex (July 2014), „The Steiner–Lehmus angle-bisector theorem“, The Mathematical Gazette, 98 (542): 193–203, doi:10.1017/s0025557200001236
- Diacu, Florin; Holmes, Philip (1999), Celestial Encounters: The Origins of Chaos and Stability, Princeton Science Library, Princeton University Press, 122-bet, ISBN 9780691005454
- Gandz, Solomon (1940), „Studies in Babylonian mathematics. III. Isoperimetric problems and the origin of the quadratic equations“, Isis, 32: 101–115 (1947), doi:10.1086/347645, MR 0017683. See in particular p. 111.
- Gilbert, G.; MacDonnell, D. (1963), „The Steiner–Lehmus Theorem“, Classroom Notes, American Mathematical Monthly, 70 (1): 79–80, doi:10.2307/2312796, MR 1531983
- Gottschau, Marinus; Haverkort, Herman; Matzke, Kilian (2018), „Reptilings and space-filling curves for acute triangles“, Discrete & Computational Geometry, 60 (1): 170–199, arXiv:1603.01382, doi:10.1007/s00454-017-9953-0
- Guinand, Andrew P. (1984), „Euler lines, tritangent centers, and their triangles“, American Mathematical Monthly, 91 (5): 290–300, doi:10.2307/2322671, MR 0740243
- Gunn, Battiscombe; Peet, T. Eric (May 1929), „Four geometrical problems from the Moscow Mathematical Papyrus“, The Journal of Egyptian Archaeology, 15 (1): 167–185, doi:10.1177/030751332901500130, JSTOR 3854111
- Hadamard, Jacques (2008), Lessons in Geometry: Plane geometry, Saul, Mark tomonidan tarjima qilingan, American Mathematical Society, ISBN 9780821843673
- Harris, John W.; Stöcker, Horst (1998), Handbook of mathematics and computational science, New York: Springer-Verlag, doi:10.1007/978-1-4612-5317-4, ISBN 0-387-94746-9, MR 1621531
- Heath, Thomas L. (1956) [1925], The Thirteen Books of Euclid's Elements, 1-jild (2nd-nashr), New York: Dover Publications, ISBN 0-486-60088-2
- Høyrup, Jens, „Geometry in Mesopotamia and Egypt“, Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, Springer Netherlands, 1019–1023-bet, doi:10.1007/978-1-4020-4425-0_8619
- Ionin, Yury J. (2009), „Isosceles sets“, Electronic Journal of Combinatorics, 16 (1): R141:1–R141:24, doi:10.37236/230, MR 2577309
- Jacobs, Harold R. (1974), Geometry, W. H. Freeman and Co., ISBN 0-7167-0456-0
- Jakway, Bernard C. (1922), The Principles of Interior Decoration, Macmillan, 48-bet
- Kahan, W. (4-sentabr 2014-yil), „Miscalculating Area and Angles of a Needle-like Triangle“ (PDF), Lecture Notes for Introductory Numerical Analysis Classes, University of California, Berkeley
{{citation}}
: CS1 maint: date format () - Ketchum, Milo Smith (1920), The Design of Highway Bridges of Steel, Timber and Concrete, New York: McGraw-Hill, 107-bet
- Langley, E. M. (1922), „Problem 644“, The Mathematical Gazette, 11: 173
- Lardner, Dionysius (1840), A Treatise on Geometry and Its Application in the Arts, The Cabinet Cyclopædia, London
- Lavedan, Pierre (1947), French Architecture, Penguin Books, 44-bet
- Loeb, Arthur (1992), Concepts and Images: Visual Mathematics, Boston: Birkhäuser Boston, 180-bet, ISBN 0-8176-3620-X
- Lord, N. J. (June 1982), „66.16 Isosceles subdivisions of triangles“, The Mathematical Gazette, 66 (436): 136, doi:10.2307/3617750
- Montroll, John (2009), Origami Polyhedra Design, A K Peters, p. 6, ISBN 9781439871065
- Oxman, Victor (2005), „On the existence of triangles with given lengths of one side, the opposite and one adjacent angle bisectors“ (PDF), Forum Geometricorum, 5: 21–22, MR 2141652, 2018-04-22da asl nusxadan (PDF) arxivlandi, qaraldi: 2021-09-30
- Padovan, Richard (2002), Towards Universality: Le Corbusier, Mies, and De Stijl, Psychology Press, 128-bet, ISBN 9780415259620
- Pellegrino, S. (2002), Deployable Structures, CISM International Centre for Mechanical Sciences, 412-jild, Springer, 99–100-bet, ISBN 9783211836859
- Posamentier, Alfred S.; Lehmann, Ingmar (2012), The Secrets of Triangles: A Mathematical Journey, Amherst, NY: Prometheus Books, 387-bet, ISBN 978-1-61614-587-3, MR 2963520
- Robbins, David P. (1995), „Areas of polygons inscribed in a circle“, American Mathematical Monthly, 102 (6): 523–530, doi:10.2307/2974766, MR 1336638
- Salvadori, Mario; Wright, Joseph P. (1998), Math Games for Middle School: Challenges and Skill-Builders for Students at Every Level, Chicago Review Press, 70–71-bet, ISBN 9781569767276
- Schwarz, H. A. (1890), Gesammelte Mathematische Abhandlungen von H. A. Schwarz, Verlag von Julius Springer, 309–311-bet
- Smith, Whitney (26-iyun 2014-yil), „Flag of Saint Lucia“, Encyclopædia Britannica, qaraldi: 2018-09-12
{{citation}}
: CS1 maint: date format () - Specht, Edward John; Jones, Harold Trainer; Calkins, Keith G.; Rhoads, Donald H. (2015), Euclidean geometry and its subgeometries, Springer, Cham, 64-bet, doi:10.1007/978-3-319-23775-6, ISBN 978-3-319-23774-9, MR 3445044
- Stahl, Saul (2003), Geometry from Euclid to Knots, Prentice-Hall, ISBN 0-13-032927-4
- Usiskin, Zalman; Griffin, Jennifer (2008), The Classification of Quadrilaterals: A Study in Definition, Research in Mathematics Education, Information Age Publishing, ISBN 9781607526001
- Venema, Gerard A. (2006), Foundations of Geometry, Prentice-Hall, ISBN 0-13-143700-3
- Washburn, Dorothy K. (July 1984), „A study of the red on cream and cream on red designs on Early Neolithic ceramics from Nea Nikomedeia“, American Journal of Archaeology, 88 (3): 305, doi:10.2307/504554
- Wickelgren, Wayne A. (2012), How to Solve Mathematical Problems, Dover Books on Mathematics, Courier Corporation, 222–224-bet, ISBN 9780486152684.
- Wilson, Robin (2008), Lewis Carroll in Numberland: His fantastical mathematical logical life, an agony in eight fits, Penguin Books, 169–170-bet, ISBN 978-0-14-101610-8, MR 2455534
- Yoshimura, Yoshimaru (July 1955), On the mechanism of buckling of a circular cylindrical shell under axial compression, Technical Memorandum 1390, National Advisory Committee for Aeronautics
- Young, Cynthia Y. (2011), Trigonometry, John Wiley & Sons, ISBN 9780470648025
Havolalar
[tahrir | manbasini tahrirlash]Weisstein, Eric W., „Teng yonli uchburchak“, MathWorld (ingl.)