Dyondzo-Tinhlayo

Dyondzo-Tinhlayo (Mathematics) (Kusuka exiGrikini μάθημα máthēma, “Vutivi, kuhlahluva, kudyondza”) idyondzo ya tinhloko-mhaka to fana ni Ntsengo (tinomboro),^[2] vuhleri,^[3] vundhawu,^[2] na macincele.^[4]^[5]^[6] kuni kuhambanahabana ka mavonele exikarhi kavan'wa-Tinhlayo na van'wa-Filisofi mayelana na nhlamuselo ya Dyondzo-Tinhlayo.^[7]^[8]

Euclid, N'wa tinhlayo wa muGriki, Lembe-xidzana ra vu3 BC, Hikuya hi Raphael.^[1]

Dyondzo-Tinhlayo iyankoka ngopfu eswiyengeni swamitirho, kuhlanganisa na ntivo-ntumbuluko, enjhiniyeringi, mirhi yavuongori, swatima kuhlanganisa na ntivo-vutomi. Kuhava ndzilakano lowuvonakalaka exikarhi ka ntivo-tinhlayo lowu tengeke na ntivo-tinhlayo lowu tirhisiwaka.^[9]

Matimu

Matimu ya dyondzo-tinhlayo yingahavoniwa tani hi tinhlamuselo tamavonele. Mavonele yosungula mafana namavonelo yaswiharhi,^[10] kungava kuri tinomboro: kutwisisa leswaku maapula mambirhi maringana hintsengo namaswira mambirhi.

Ehenhleni kokota ku hlaya swilo leswivonakaka, vanhu vakhale avaswikota kuhlaya naleswi vangaswivoniki, kufana na nkarhi, masiku, tinguva namalembe.^[11]

Kuhava vumboni bya dyondzo-tinhlayo kufikela eka lembe ra 3000 BC, loko va aki vaBabilona na va aki va Gibhita vasungula to tirhisa aritimatiki (Nhlayo-Vunyingi), aljebra (Nhlayo-vuringanisi) na Jiyometiri (Nhlayo-Vuaki) leswaku vahlengeleta xibhalo, kuhlaya mali, naku aka, kuhlanganisa na ntivo-tinyeleti.^[12] The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns and the recording of time.

Mintshaho

↑ No likeness or description of Euclid's physical appearance made during his lifetime survived antiquity.
↑ ^2.0 ^2.1 "mathematics, n.". Oxford English Dictionary. Oxford University Press. 2012. Retrieved June 16, 2012. "The science of space, number, quantity, and arrangement, whose methods involve logical reasoning and usually the use of symbolic notation, and which includes geometry, arithmetic, algebra, and analysis."
↑ Kneebone, G.T. (1963). Mathematical Logic and the Foundations of Mathematics: An Introductory Survey. Dover. pp. 4. ISBN 0-486-41712-3. "Mathematics ... is simply the study of abstract structures, or formal patterns of connectedness."
↑ LaTorre, Donald R., John W. Kenelly, Iris B. Reed, Laurel R. Carpenter, and Cynthia R Harris (2011). Calculus Concepts: An Informal Approach to the Mathematics of Change. Cengage Learning. pp. 2. ISBN 1-4390-4957-2. "Calculus is the study of change—how things change, and how quickly they change."
↑ Ramana (2007). Applied Mathematics. Tata McGraw–Hill Education. p. 2.10. ISBN 0-07-066753-5. "The mathematical study of change, motion, growth or decay is calculus."
↑ Ziegler, Günter M. (2011). "What Is Mathematics?". An Invitation to Mathematics: From Competitions to Research. Springer. pp. 7. ISBN 3-642-19532-6.
↑ Mura, Roberta (Dec 1993). "Images of Mathematics Held by University Teachers of Mathematical Sciences". Educational Studies in Mathematics 25 (4): 375–385.
↑ Tobies, Renate and Helmut Neunzert (2012). Iris Runge: A Life at the Crossroads of Mathematics, Science, and Industry. Springer. pp. 9. ISBN 3-0348-0229-3. "It is first necessary to ask what is meant by mathematics in general. Illustrious scholars have debated this matter until they were blue in the face, and yet no consensus has been reached about whether mathematics is a natural science, a branch of the humanities, or an art form."
↑ Peterson
↑ Dehaene, Stanislas; Dehaene-Lambertz, Ghislaine; Cohen, Laurent (Aug 1998). "Abstract representations of numbers in the animal and human brain". Trends in Neuroscience 21 (8): 355–361. PMID 9720604. doi:10.1016/S0166-2236(98)01263-6.
↑ See, for example, Raymond L. Wilder, Evolution of Mathematical Concepts; an Elementary Study, passim
↑ Kline 1990, Chapter 1.

[1] No likeness or description of Euclid's physical appearance made during his lifetime survived antiquity.

[OED-2] 2.0 ^2.1 "mathematics, n.". Oxford English Dictionary. Oxford University Press. 2012. Retrieved June 16, 2012. "The science of space, number, quantity, and arrangement, whose methods involve logical reasoning and usually the use of symbolic notation, and which includes geometry, arithmetic, algebra, and analysis."

[Kneebone-3] Kneebone, G.T. (1963). Mathematical Logic and the Foundations of Mathematics: An Introductory Survey. Dover. pp. 4. ISBN 0-486-41712-3. "Mathematics ... is simply the study of abstract structures, or formal patterns of connectedness."

[LaTorre-4] LaTorre, Donald R., John W. Kenelly, Iris B. Reed, Laurel R. Carpenter, and Cynthia R Harris (2011). Calculus Concepts: An Informal Approach to the Mathematics of Change. Cengage Learning. pp. 2. ISBN 1-4390-4957-2. "Calculus is the study of change—how things change, and how quickly they change."

[Ramana-5] Ramana (2007). Applied Mathematics. Tata McGraw–Hill Education. p. 2.10. ISBN 0-07-066753-5. "The mathematical study of change, motion, growth or decay is calculus."

[Ziegler-6] Ziegler, Günter M. (2011). "What Is Mathematics?". An Invitation to Mathematics: From Competitions to Research. Springer. pp. 7. ISBN 3-642-19532-6.

[Mura-7] Mura, Roberta (Dec 1993). "Images of Mathematics Held by University Teachers of Mathematical Sciences". Educational Studies in Mathematics 25 (4): 375–385.

[Runge-8] Tobies, Renate and Helmut Neunzert (2012). Iris Runge: A Life at the Crossroads of Mathematics, Science, and Industry. Springer. pp. 9. ISBN 3-0348-0229-3. "It is first necessary to ask what is meant by mathematics in general. Illustrious scholars have debated this matter until they were blue in the face, and yet no consensus has been reached about whether mathematics is a natural science, a branch of the humanities, or an art form."

[9] Peterson

[10] Dehaene, Stanislas; Dehaene-Lambertz, Ghislaine; Cohen, Laurent (Aug 1998). "Abstract representations of numbers in the animal and human brain". Trends in Neuroscience 21 (8): 355–361. PMID 9720604. doi:10.1016/S0166-2236(98)01263-6.

[11] See, for example, Raymond L. Wilder, Evolution of Mathematical Concepts; an Elementary Study, passim

[12] Kline 1990, Chapter 1.

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