Karl Weierstrass - Alchetron, The Free Social Encyclopedia
Karl Weierstrass - Alchetron, The Free Social Encyclopedia
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Karl Weierstrass Biography | Pantheon
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1872 में जर्मन गणितज्ञ कार्ल वीयरश्ट्रास (Karl Weierstrass) ने एक ऐसा अद्भुत फलन (function) प्रस्तुत किया जो हर बिंदु पर सतत (continuous) था, लेकिन किसी भी बिंदु पर अवकलनीय (differentiable) नहीं था। इस खोज ने उस समय की आम धारणा को तोड़ दिया — कि कोई भी सतत रेखा ज़्यादातर स्थानों पर चिकनी (smooth) होनी चाहिए। वीयरश्ट्रास के इस उदाहरण ने गणितज्ञों की सोच को बदल दिया और गणितीय विश्लेषण (mathematical analysis) के क्षेत्र में एक नया युग शुरू किया। इस फलन ने यह दिखाया कि निरंतरता (continuity) और अवकलन
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1872 में जर्मन गणितज्ञ कार्ल वीयरश्ट्रास (Karl Wei…
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SOLVED:The German mathematician Karl Weierstrass (1815-1897) noticed that the substitution t=tan(x / 2) will convert any rational function of sinx and cosx into an ordinary rational function of t . (a) If t=tan (x / 2),-π<x<π, sketch a right triangle or use trigonometric identities to show that cos((x)/(2))=(1)/(√(1 t^2)) and sin((x)/(2))=(t)/(√(1 t^2)) (b) Show that cosx=(1-t^2)/(1 t^2) and sinx=(2 t)/(1 t^2) (c) Show that d x=(2)/(1 t^2) d t
SOLVED:The German mathematician Karl Weierstrass (1…
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