srki function

Jan 2012
80
0
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
 
Jan 2012
80
0
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
 
Jan 2012
80
0
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
 
Jan 2012
80
0
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
 
Jan 2012
80
0
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)
 
Jan 2012
80
0
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)