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Thread: srki function

  1. #1
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    srki function

    your comment, which is attached
    srki_function.pdfsrki_function.pdf
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  2. #2
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    Re: srki function

    srki function is a secondary function, derived from a function and a defined geometric object.


    download program geogebra

    an attachment in which the srki functions are described, you choose the function f (x), you choose free point C, the independent variable x (represents the point A) that you move freely,
    www.geogebra.org/m/D9ZxQX7J
    turn on the "show trace" in the long (i) and BC, for some interval (a, b), you get different geometric objects, which represents a srki integral, and can be a topography transition from a long to a surface object, can be specified as a constant or a srki function integral
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  3. #3
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    Re: srki function

    an attachment in which the srki functions are described, you choose the function f (x), you choose free point C, the independent variable x (represents the point A) that you move freely,the values of C = (a, b) must be manually replaced in $p(x)=\sqrt{(x-a)^2+(f(x)-b)^2}$

    www.geogebra.org/m/Aus2EE83

    turn on the "show trace" in the tright line CD and BC, for some interval (a, b), you get different geometric objects

    SUMMARY

    $\widehat{x_1(a,b)}$
    $\widehat{x_2(x,f(x))}$
    $\widehat{s_1}=\sqrt{(x-a)^2+(f(x)-b)^2}$ - srki function
    $\widehat{s_2}=\sqrt{(x-a)^2+(f({\widehat{s_1}})-b)^2}$ - second srki function
    $\widehat{s_3}=\sqrt{(x-a)^2+(f(\widehat{s_2})-b)^2}$ - third srki function
    $...$

    derived things from the srki function:
    - n-srki integrals
    -derivatives srki integrals as a union, intersection, difference srki integrals
    - srki integral function as a constant and variable
    function of the srki integral derivative as a constant and variable
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  4. #4
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    Re: srki function

    conditions:

    $\widehat{x_1(x+a,x"x+a"f(x))}$ or $\widehat{x_1(x-a,x"x-a"f(x))}$
    $\widehat{x_2(x,f(x))}$
    $\widehat{s_1}=\sqrt{(x-(x+a))^2+(f(x)-(x"x+a"f(x))^2}$ or $\widehat{s_1}=\sqrt{(x-(x-a))^2+(f(x)-(x"x-a"f(x))^2}$

    an attachment in which the heart functions are described, you select the function f (x), the independent variable x (moves point A), move the "show trace" on BD for a certain interval (a, b), get different geometric objects
    https://www.geogebra.org/m/Y9j2ApnQ

    new term $ x"x+a"f(x)$ , which means that there is a substitute $x$ for $x+a$ in the function of $f(x)$
    $f(x)=2x^2-4 ""2(x+a)^2-4$

    an attachment in which the heart functions are described, you choose the function f (x), the independent variable x (moves point A), move the "show trace" on longer BD and DE for some interval (a, b), you get different geometric objects
    https://www.geogebra.org/m/JHpW5xSn
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  5. #5
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    Re: srki function

    error instead of this
    https://www.geogebra.org/m/JHpW5xSn
    should be
    https://www.geogebra.org/m/XdR5Vhk4

    an attachment in which the heart functions are described, you choose the function f (x), the independent variable x (moves point A), move the "show trace" on longer BD and EF for some interval (a, b), you get different geometric objects
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  6. #6
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    Re: srki function

    conditions:

    $\widehat{x_1(x+p(x),x"x+p(x)"f(x))}$ or $\widehat{x_1(x-p(x),x"x-p(x)"f(x))}$
    $\widehat{x_2(x,f(x))}$
    $\widehat{s_1}=\sqrt{(x-(x+p(x)))^2+(f(x)-(x"x+p(x)"f(x))^2}$ or $\widehat{s_1}=\sqrt{(x-(x-p(x)))^2+(f(x)-(x"x-p(x)"f(x))^2}$

    I could not move graphically on a geogebra, the functions f (x) and p (x) are independent of each other
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  7. #7
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    Re: srki function

    conditions:
    $\widehat{x_1(E_2)}$ or $\widehat{x_1(E_1)}$
    $\widehat{x_2(x,f(x))}$
    $\widehat{s_1}=\sqrt{(x-E_2)^2+(f(x)-E_2)^2}$ or $\widehat{s_1}=\sqrt{(x-E_1)^2+(f(x)-E_1)^2}$

    an attachment https://www.geogebra.org/m/h2p7Uu6m

    $E_2,E_1$ I did not find an algebraic procedure for a circle (a constant radius) and a function f (x), if you know how to set it, but I solved it on a geogebra (attached)
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  8. #8
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    Re: srki function

    conditions:
    $\widehat{x_1(E_2)}$ or $\widehat{x_1(E_1)}$
    $\widehat{x_2(x,f(x))}$
    $\widehat{s_1}=\sqrt{(x-E_2)^2+(f(x)-E_2)^2}$ or $\widehat{s_1}=\sqrt{(x-E_1)^2+(f(x)-E_1)^2}$

    an attachment https://www.geogebra.org/m/zWneK4hm

    $E_2,E_1$ I did not find an algebraic procedure for a circle (variable radius |x|) and a function f (x), if you know how to set it, but I solved it on a geogebra (attached)
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