What is the Number e?



You know all about pi, but have you ever heard of the number e? Let’s take a look at this interesting and important mathematical constant.

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This video was made in association with the Math Centre at Humber College

Drawing, script and editing by Tyler Sy
Final production editing by Katie VanderLaan
Producer – Cameron Redsell-Montgomerie

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45 Comments

  1. Another interesting quality of e: The simple exponential function of base e, that is, f(x) = e^x, is the only nonconstant function whose derivative evaluated at any given value of x equals the value of the function at that value of x. Put another way, at any given point on the curve of f(x) = e^x, the slope of the tangent line to the curve EQUALS the height of the curve above the x-axis.

  2. Also:
    d(e^x) = e^xdx
    e^(λx) is the general formula for the solutions of an ordinary differential equation.
    ln(x), or log_e(x) = ∫(1, x)dt/t
    Euler's Formula: e^(πi)+1 = 0, cos(x) = cosh(ix), sin(x) = -i*sinh(ix)

  3. Two numbers number 1

    e0.3678794411714423215955237701614608674458111310317678345078368016974614957448998033571472743459196437466273252768439952082469757927901290086266535894940987830921943673773381150486389911251456163449877199786844759579397473025498924954532393662079648105146475206122942230891649265666003650745772837055328537383881068047876119568298934544973507393185992166174330035699372082071022775180215849942337816907156676717623366082303761229156237572094700070405097334256775762525280303768861651570936537995427406370717878445419467490931306980560163702111389774228214017380232832465287291389004660986659512444097699851459164287803720202510224578732111059537776807437112206240005167965280975444780286486006838564200433684662484349386918262062518994821970992423425207510492093445285124486022451380986417421061219536368310078209224804653079806562854154786061793155705987170215999699188228265397927803747127438635156296714511943986702682452679716814389772141359579690542529103548859731078233269414118579235695949376986012657588031279984679484673513468022653024462770569824438638729700298758880953411267542378902616433104091860701225717581666034510079098588808084286840740013403838132000405677583140619926558491845127806870837819198202812845022642081730224354601095412338871575982537376825937442618108261974718650463417452873248272637661583763933421278629358444618677226500353035131097140226114592021137432096713055954505147204649927608239102334732395201495304468001908089101037412807847539359160611641079862219291665624157281

    Number 2

    e0.3678794411714423215955237701614608674458111310317678345078368016974614957448998033571472743459196437466273252768439952082469757927901290086266535894940987830921943673773381150486389911251456163449877199786844759579397473025498924954532393662079648105146475206122942230891649265666003650745772837055328537383881068047876119568298934544973507393185992166174330035699372082071022775180215849942337816907156676717623366082303761229156237572094700070405097334256775762525280303768861651570936537995427406370717878445419467490931306980560163702111389774228214017380232832465287291389004660986659512444097699851459164287803720202510224578732111059537776807437112206240005167965280975444780286486006838564200433684662484349386918262062518994821970992423425207510492093445285124486022451380986417421061219536368310078209224804653079806562854154786061793155705987170215999699188228265397927803747127438635156296714511943986702682452679716814389772141359579690542529103548859731078233269414118579235695949376986012657588031279984679484673513468022653024462770569824438638729700298758880953411267542378902616433104091860701225717581666034510079098588808084286840740013403838132000405677583140619926558491845127806870837819198202812845022642081730224354601095412338871575982537376825937442618108261974718650463417452873248272637661583763933421278629358444618677226500353035131097140226114592021137432096713055954505147204649927608239102334732395201495304468001908089101037412807847539359160611641079862219291665624157280

  4. Increasing an amount by infant accessibly small breaks in interest. You get E.

    It describes the normal distribution and statistics
    Biology and models population
    And physics, it defines the radioactive decay of a material

  5. HOLY CRAP YOU HAVE DISCRIBED THE ORIGINAL REASON WHY THE CONCEPT OF e SHOULD HAVE BEEN INVENTED… IVE NEVER HEARD ABOUT THIS BEFORE IN THE SCHOOL NEITHER IN THE COLLEAGUE

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