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Georg Friedrich Bernhard Riemann was a prominent German mathematician known for his contributions to various fields, including analysis, differential geometry, and number theory. He formulated the Riemann hypothesis, one of the most important unsolved problems in mathematics, which relates to the distribution of prime numbers. His work on Riemann surfaces laid the groundwork for modern complex analysis, while his contributions to Riemannian geometry have had a profound impact on the development of general relativity. Additionally, Riemann introduced the concept of the integral that bears his name, advancing the understanding of convergence in analysis.
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Who was the most popular mathematician?
This is impossible to give as a fact as everybody will have a different opinion. the top ten is 1. Leonhard Euler 2. Carl Friedrich Gauss 3. G. F. Bernhard Riemann 4. Euclid 5. René Descartes 6. Alan Turing 7. Leonardo Pisano Blgollo (a.k.a. Leonardo Fibonacci) 8. Isaac Newton and Wilhelm Leibniz 9. Andrew Wiles 10. Pythagoras
Rules of differentiation?
Assume f=f(x), g=g(x)and (f^-1)(x) is the functional inverse of f(x). (f+g)'=f'+g' (f*g)'=f'*g+f*g' product rule (f(g))'=g'*f'(g) compositional rule (f/g)'=(f'*g-f*g')/(g^2) quotient rule (d/dx)(x^r)=r*x^(r-1) power rule and applies for ALL r. where g^2 is g*g not g(g)
In the function g f x f depends on g and g depends on x?
In the function ( g(f(x)) ), ( f ) is a function that takes ( x ) as input and produces an output used as input for ( g ). Here, ( g ) depends on the output of ( f ), meaning that ( g ) processes the result obtained from ( f(x) ). Consequently, the overall function ( g(f(x)) ) showcases a composition where the behavior of ( g ) is influenced by the behavior of ( f ) in relation to ( x ).
When was Pierre De fermat's last theorem created?
PIERRE DE FERMAT's last Theorem. (x,y,z,n) belong ( N+ )^4.. n>2. (a) belong Z F is function of ( a.) F(a)=[a(a+1)/2]^2 F(0)=0 and F(-1)=0. Consider two equations F(z)=F(x)+F(y) F(z-1)=F(x-1)+F(y-1) We have a string inference F(z)=F(x)+F(y) equivalent F(z-1)=F(x-1)+F(y-1) F(z)=F(x)+F(y) infer F(z-1)=F(x-1)+F(y-1) F(z-x-1)=F(x-x-1)+F(y-x-1) infer F(z-x-2)=F(x-x-2)+F(y-x-2) we see F(z-x-1)=F(x-x-1)+F(y-x-1 ) F(z-x-1)=F(-1)+F(y-x-1 ) F(z-x-1)=0+F(y-x-1 ) give z=y and F(z-x-2)=F(x-x-2)+F(y-x-2) F(z-x-2)=F(-2)+F(y-x-2) F(z-x-2)=1+F(y-x-2) give z=/=y. So F(z-x-1)=F(x-x-1)+F(y-x-1) don't infer F(z-x-2)=F(x-x-2)+F(y-x-2) So F(z)=F(x)+F(y) don't infer F(z-1)=F(x-1)+F(y-1) So F(z)=F(x)+F(y) is not equivalent F(z-1)=F(x-1)+F(y-1) So have two cases. [F(x)+F(y)] = F(z) and F(x-1)+F(y-1)]=/=F(z-1) or vice versa So [F(x)+F(y)]-[F(x-1)+F(y-1)]=/=F(z)-F(z-1). Or F(x)-F(x-1)+F(y)-F(y-1)=/=F(z)-F(z-1). We have F(x)-F(x-1) =[x(x+1)/2]^2 - [(x-1)x/2]^2. =(x^4+2x^3+x^2/4) - (x^4-2x^3+x^2/4). =x^3. F(y)-F(y-1) =y^3. F(z)-F(z-1) =z^3. So x^3+y^3=/=z^3. n>2. .Similar. We have a string inference G(z)*F(z)=G(x)*F(x)+G(y)*F(y) equivalent G(z)*F(z-1)=G(x)*F(x-1)+G(y)*F(y-1) G(z)*F(z)=G(x)*F(x)+G(y)*F(y) infer G(z)*F(z-1)=G(x)*F(x-1)+G(y)*F(y-1) G(z)*F(z-x-1)=G(x)*F(x-x-1)+G(y-x-1)*F(y) infer G(z)*F(z-x-2)=G(x)*F(x-x-2)+G(y)*F(y-x-2) we see G(z)*F(z-x-1)=G(x)*F(x-x-1)+G(y)*F(y-x-1 ) G(z)*F(z-x-1)=G(x)*F(-1)+G(y)*F(y-x-1 ) G(z)*F(z-x-1)=0+G(y)*F(y-x-1 ) give z=y. and G(z)*F(z-x-2)=G(x)*F(x-x-2)+G(y)*F(y-x-2) G(z)*F(z-x-2)=G(x)*F(-2)+G(y)*F(y-x-2) G(z)*F(z-x-2)=G(x)+G(y)*F(y-x-2) x>0 infer G(x)>0. give z=/=y. So G(z)*F(z-x-1)=G(x)*F(x-x-1)+G(y-x-1)*F(y) don't infer G(z)*F(z-x-2)=G(x)*F(x-x-2)+G(y)*F(y-x-2) So G(z)*F(z)=G(x)*F(x)+G(y)*F(y) don't infer G(z)*F(z-1)=G(x)*F(x-1)+G(y)*F(y-1) So G(z)*F(z)=G(x)*F(x)+G(y)*F(y) is not equiivalent G(z)*F(z-1)=G(x)*F(x-1)+G(y)*F(y-1) So have two cases [G(x)*F(x)+G(y)*F(y)]=G(z)*F(z) and [ G(x)*F(x-1)+G(y)*F(y-1)]=/=G(z-1)*F(z-1) or vice versa. So [G(x)*F(x)+G(y)*F(y)] - [ G(x)*F(x-1)+G(y)*F(y-1)]=/=G(z)*[F(z)-F(z-1)]. Or G(x)*[F(x) - F(x-1)] + G(y)*[F(y)-F(y-1)]=/=G(z)*[F(z)-F(z-1).] We have x^n=G(x)*[F(x)-F(x-1) ] y^n=G(y)*[F(y)-F(y-1) ] z^n=G(z)*[F(z)-F(z-1) ] So x^n+y^n=/=z^n Happy&Peace. Trần Tấn Cường.
What describes the product rule?
The product rule for derivatives is as follows. For the derivative of the product of two functions, "f" and "g":(f times g)' = f times g' + f' times g
What did g f bernhard riemann discover?
dont no
What has the author G Riemann written?
G. Riemann has written: 'Die taubstumm-blinden' -- subject(s): Blind, Deaf, Education
What nicknames does Bernhard Gaudian go by?
Bernhard Gaudian goes by Bernie G.
How do you play what makes you beautiful on a recorder?
a-g-f-f-f-f-f-f-f-g-a-g-a-g-f-f-f-f-f-f-f-f-f-a-g-g-a-g-f-f-g-a-a-a-a-a-a-g-f
How do you play what makes you beautiful on recorder?
a-g-f-f-f-f-f-f-f-g-a-g-a-g-f-f-f-f-f-f-f-f-f-a-g-g-a-g-f-f-g-a-a-a-a-a-a-g-f that is only chorus
How do you play baby on flute?
Baby by: Justin BieberF G F F A G F E D E D F A G F E D E D F A G F G G F EF C2 A G A F C2 A G F C2 A G A F C2 A G F C2 C2 A G F C2 C2 A GF F A G A G A G A G A G F C2 A G A C2 A G F C2 G A F F G F F F A A G F GF F G G G G G G A G F F G FChorus: A G A G A G C2 G A G A G A G D2 G A G A G A G C2 A G A A A G FA G A G A G C2 G A G A G A G D2 G A G A G A G C2 A G A A A G F-Rossele-Send more requests @ycel_gandah@Yahoo.comTy!
What are the notes to fireflies on a trumpet?
C g g f g f c c d d c d f g a g f c c g f d c g g f g f c d d c d f g c c a g f c a g d f a g f c a g f g c f e d c e d c d f a g f d d f a g c d f f a g f d f g c g g f g f c c d d c d f g a g f c a g f d c g g f g f c d d c d f g c c a g f c a g d f a g f c a g f g c f e d c e d c d f a g f d d f a g c d f f a g f d f g c g f g f g f c c d f c d f c g g-f g-f g-a-f c d f c d f c g g-f g-f g-f-d c d f c d f c g g-f g-f g-a-f
How do you play baby on the flute?
Baby by: Justin BieberF G F F A G F E D E D F A G F E D E D F A G F G G F EF C2 A G A F C2 A G F C2 A G A F C2 A G F C2 C2 A G F C2 C2 A GF F A G A G A G A G A G F C2 A G A C2 A G F C2 G A F F G F F F A A G F GF F G G G G G G A G F F G FChorus: A G A G A G C2 G A G A G A G D2 G A G A G A G C2 A G A A A G FA G A G A G C2 G A G A G A G D2 G A G A G A G C2 A G A A A G F-Rossele-Send more requests @ycel_gandah@yahoo.comTy!
What is the keyboard notes for just the way you are?
C c f g ac f g a g f g ff f g a g b a f g fc f g ac f g a g f f g ff f g a g b a f g f
What are the piano notes for if i ain't got you?
right hand:E G F G F G G G G G G G G Left hand G F F F F F G F F F E E
What has the author Bernhard G Funck written?
Bernhard G. Funck has written: 'Konflikte im Steuerrecht' -- subject(s): Taxation, Law and legislation, Tax administration and procedure
What are the piano notes for mad world?
Gary Jules version: (based off a tab by slippy) Acoustic Grand Piano. 5|---c--------------------|-----------------------| 4|G--g--g--G--f--g--D--d--|------f-----------f--G-| 4|------c--g-----f--c-----|------d-----------d----| 3|f-----G-----f-----G-----|A-----------A----------| 5|---c--------------------|------------------------|------------------------| 4|---g--g--G--f--g--G--A--|------f-----------f-----|------f--f--G--G--f--f--| 4|------c--g-----f--c--f--|------d-----------d-----|------c-----------c-----| 3|f-----G-----f-----G-----|A-----------A-----------|f-----G-----f-----G-----| 5|c--c-----c-------------|-----------------------| 4|------D--------G--D----|A--A-----A-----g-------| 4|------c-----------c----|-----------------------| 3|G-----------G----------|D-----g-----D-----A----| 3|-----------------------|------A-----------g----| 4|A--A--f--A-----G--g---f---|-----f--f--G--G--f--f--| 4|------d-----------f-------|-----c-----------c-----| 4|------------------d-------|-----------------------| 3|A-----------A-------------|f----G-----f-----G-----| 5|c--c-----c-------------|-----------------------| 4|------D--------G--D----|A--A-----A-----g-------| 4|------c-----------c----|-----------------------| 3|G-----------G----------|D-----g-----D-----A----| 3|-----------------------|------A-----------g----| 4|A--A--f--A-----G--g---f---|-----f--f--G--G--f--f--| 4|------d-----------f-------|-----c-----------c-----| 4|------------------d-------|-----------------------| 3|A-----------A-------------|f----G-----f-----G-----| 5|c--c-----c-------------|-----------------------| 4|------D--------G--D----|A--A-----A-----g-------| 4|------c-----------c----|-----------------------| 3|G-----------G----------|D-----g-----D-----A----| 3|-----------------------|------A-----------g----| 4|A--A--f--A-----G--g---f---|-----f--f--G--G--f--f--| 4|------d-----------f-------|-----c-----------c-----| 4|------------------d-------|-----------------------| 3|A-----------A-------------|f----G-----f-----G-----| 5|c--c-----c-------------|-----------------------|----------------------| 4|------D--------G--D----|A--A-----A-----g-------|A--A----A----G--g--f--| 4|------c-----------c----|-----------------------|f---------------------| 4|-----------------------|-----------------------|d---------------------| 3|G-----------G----------|D-----g-----D-----A----|A---------------------| 3|-----------------------|------A-----------g----|----------------------| 5|-----------------c---c---|d---------------d---d----------| 4|G----f--f--G--G--G---G---|f---A---f---A---f---f---A---A--| 4|f----c-----f--f--f---f---|----f---d---f-----------f---f--| 4|-----------------c-------|------------------------f------| 4|-------------------------|------------------------d------| 3|f----G-----f-----G-------|A---------------A--------------| 5|------------------c---c---|d--------------d---d----------| 4|G-----f--f--G--G--G---G---|f---A---A---A--f---f---A---A--| 4|f-----c-----f--f--f---f---|----f---f---f----------f---f--| 4|------------------c-------|--------f--------------f------| 4|--------------------------|--------d--------------d------| 3|f-----G-----f-----G-------|A--------------A--------------| 5|------------------c---c---|d---------------d---d----------| 4|G-----f--f--G--G--G---G---|f---A---f---A---f---f---A---A--| 4|f-----c-----f--f--f---f---|----f---d---f-----------f---f--| 4|------------------c-------|------------------------f------| 4|--------------------------|------------------------d------| 3|f-----G-----f-----G-------|A---------------A--------------| 5|------------------c---c---|d---------------d---d-----------| 4|G-----f--f--G--G--G---G---|f---A---A---A---f---f---A---A---| 4|f-----c-----f--f--f---f---|f---f---f---f-----------f---f---| 4|------------------c-------|d-------------------------------| 3|f-----G-----f-----G-------|A-------------------------------| 5|---c-----------------------|---------------------| 4|G--g--g--G---G---g---D--d--|f----f---------f--G--| 4|------c--g---f---f---c-----|-----d---------d-----| 3|f-----G------f-------G-----|A---------A----------| 5|---c-------------------------|--------------------| 4|---g--g--G---G---g---G---A---|-----f---------f----| 4|------c--g---f---f---c---f---|-----d---------d----| 3|f-----G------f-------G-------|A---------A---------| 5|-----------------------|c--c-----c--------------|-----------------------| 4|-----f--f--G--G--f--f--|------D--------G--D-----|A--A-----A-----g-------| 4|-----c-----------------|------c-----------c-----|-----------------------| 3|f----G-----f-----------|G-----------G-----------|D-----A-----D-----A----| 3|-----------------------|------------c-----------|------g-----------g----| 2|f----------------f-----|G-----------------------|-----------------------| 4|A--A--f--A-----G--g---f---|-----f--f--G--G--f--f--| 4|------d-----------f-------|-----c-----------------| 4|------------------d-------|-----------------------| 3|A-----------A-------------|f----G-----f-----------| 3|d-------------------------|-----------------------| 2|--------------------------|f----------------f-----| 5|c--c-----c--------------|-----------------------| 4|------D--------G--D-----|A--A-----A-----g-------| 4|------c-----------c-----|-----------------------| 3|G-----------G-----------|D-----A-----D-----A----| 3|------------c-----------|------g-----------g----| 2|G-----------------------|-----------------------| 4|A--A--f--A-----G--g---f---|-----f--f--G--G--f--f--| 4|------d-----------f-------|-----c-----------------| 4|------------------d-------|-----------------------| 3|d-------------------------|-----------------------| 2|--------------------------|f----------------g-----| 5|c--c-----c--------------|-----------------------| 4|------D--------G--D-----|A--A-----A-----g-------| 4|------c-----------c-----|-----------------------| 3|G-----------G-----------|D-----A-----D-----A----| 3|------------c-----------|------g-----------g----| 2|G-----------------------|-----------------------| 4|A--A--f--A-----G--g---f---|-----f--f--G--G--f--f--| 4|------d-----------f-------|-----c-----------------| 4|------------------d-------|-----------------------| 3|A-----------A-------------|f----G-----f-----------| 3|d-------------------------|-----------------------| 2|--------------------------|f----------------f-----| 5|c--c-----c--------------|-----------------------|----------------------| 4|------D--------G--D-----|A--A-----A-----g-------|A--A----A----G--g--f--| 4|------c-----------c-----|-----------------------|f---------------------| 4|------------------------|-----------------------|d---------------------| 3|G-----------G-----------|D-----A-----D-----A----|A---------------------| 3|------------c-----------|------g-----------g----|----------------------| 2|G-----------------------|-----------------------|----------------------| 5|-----------------c---c---|d------------d---d----------| 4|G----f--f--G--G--G---G---|f---A--f--A--f---f---A---A--| 4|f----c-----f--f--f---f---|----f--d--f----------f---f--| 4|-----------------c-------|---------------------f------| 4|-------------------------|---------------------d------| 3|f----G-----f-----G-------|A------------A--------------| 2|f------------------------|A---------------------------| 5|-----------------c---c---|d-------------d---d----------| 4|G----f--f--G--G--G---G---|f---A--A---A--f---f---A---A--| 4|f----c-----f--f--f---f---|----f--f---f----------f---f--| 4|-----------------c-------|-------f--------------f------| 4|-------------------------|-------d--------------d------| 3|f----G-----f-----G-------|A-------------A--------------| 2|f------------------------|A----------------------------| 5|-----------------c---c---|d------------d---d----------| 4|G----f--f--G--G--G---G---|f---A--f--A--f---f---A---A--| 4|f----c-----f--f--f---f---|----f--d--f----------f---f--| 4|-----------------c-------|---------------------f------| 4|-------------------------|---------------------d------| 3|f----G-----f-----G-------|A------------A--------------| 2|f------------------------|A---------------------------| 5|-----------------c---c---|d---------------d---d-----------| 4|G----f--f--G--G--G---G---|f---A---A---A---f---f---A---A---| 4|f----c-----f--f--f---f---|f---f---f---f-----------f---f---| 4|-----------------c-------|d-------------------------------| 3|f----G-----f-----G-------|A-------------------------------| 2|f------------------------|--------------------------------| 5|---c-----------------------|---------------------| 4|G--g--g--G---G---g---D--d--|f----f---------f--G--| 4|------c--g---f---f---c-----|-----d---------d-----| 3|f-----G------f-------G-----|A---------A----------| 5|---c-------------------------|--------------------| 4|---g--g--G---G---g---G---A---|-----f---------f----| 4|------c--g---f---f---c---f---|-----d---------d----| 3|f-----G------f-------G-------|A---------A---------| 5|---c-----------------------|--------------------| 4|G--g--g--G---G---g---D--d--|f----f---------f----| 4|------c--g---f---f---c-----|-----d---------d----| 3|f-----G------f-------G-----|A---------A---------| 4|G--G--g---g---f---f---D---d--|----------------- 4|------c---------------c------|----------------- 3|f-----G-------f-------G------|A---------------- 3|-----------------------------|f---------------- 2|-----------------------------|A---------------- < I found this very helpful and many thank you both slippy and Katie for all their hardwork!> Sungod357 Gary jules: Mad world Beginning: G# up to C down to G up to G# down to F up to G down to D# down to D down to A# up to D down to A# up to D (2 times) G# up to C down to G up to G# down to F up to G up to G# up to A# down to A# up to D down to A# up to D --------------------------------------------------------- a more advanced version with chords and stuff: On the left hand play the "G# up to C down to G up to G# down to F up to G down to D# down to D" bit except instead of "down to A# up to D down to A# up to D", Do A# then D and F at the same time. Meanwhile, your right hand plays this chord F and then G# and C Okay mad. Try this now. F F G# G# F F C C C G# A# A# A# G A# A# A# G# G F repeat it a few times
