   The upgraded GEOMECA 4e (version 4.1) HTML Help is in one HTML Help in Korean and English. (It's in the product.) Within the program, you can use it by switching to Korean or English, like version 5.   The HTML Help for the upgraded GEOMECA 5 (version 5.0) was created first only in Korean. (It's in the product.) You can use it by converting it into Korean or English within the program.   Click the three buttons below to see a screenshot of HTML Help.  What can this program do? How can  this program be applied? Summary of function of Version 4..0? How to use (Simple explanation) How to use: The 1st: Drawing the graph of functions; 1 - line, point, cylindrical unit Two regular octahedrons    - Ray trace    - opacity, semitranceparancy The 4th: Drawing the graph of  functions; 4 - surface The 5th: Drawing other graphs; 5 - pentagonal prism (using commands) The 6th: Trace of fucntion values of a curve or a surface The 7th: Drawing a graph by transforming The 8th: To use the collection of executed formulas and a picture collection screen; 1 The 9th: To use a picture collection screen; 2 and print, save The 10th: Making lines to be rotated using the muli-line of figure tools and makiing a body of rotation The 11th : To use differentiation The 12th: To use complex numbers, integral, parametric (multivariable) function formulas, scientic calculation and other calculations The 13th: To use matrix calculation The 14th: To perform statistical calculations The 15th: To draw included functions; To apply the basic editing of pictures

 Function (Picture explanation): What's new in version 4.0 ? Function Expression input Rectangular coordinates Curve 2 dim Negative f(x,y)=0 3-dimensional solid curve can be made.   3-dimensional surface: perfectly Surface 3 dim Negative f(x,y,z)=0 Polar coordinates Curve 2 dim Negative   f(r,u)=0 Sphere coordinates Cylindrical coordinates Curve 3 dim Parametric r=f(u): p=g(u):  z=h(u) Surface 3 dim Parametric r=f(u,v): p=g(u,v):  z=h(u,v) Other figures Curve 2,3 dim Surface solid 2,3 dim Figure Tools: Drawing things such as basic figures, functions, quadric curves, etc. in 2- or 3-dimensional coordinates by using the mouse. A body of rotation - Rotating lines that are drawn by the function-expression or figure tools or commands.   Making a body of rotation centering around  the rotation-axis which is the axis of x, y, z or any line or the line through two points  appointed by the angle and subdivision. The drawing screen Adjusting the size of coordinates region 2-dimensional coordinates The method displaying 2- dimensional coordinates Displaying the polar coordinates Displaying the arrowheads: auto-option Displaying  the origin, axis, coordinates values auto - option The method displaying 3-dimensional coordinates Drawing the space-frame, the coordinates-axis 3D Displaying a full line or a dotted line of  the space- frame temporarily (Not) displaying middle lines of the surface of the space-frame Making selected items be continuously seen when we let the space-frame be rotated (animation) Displaying coordinates values auto - option Equally dividing interval of variable range; adjusting subdivision of figure for velocity, accuracy, good picture 4.0 can re-adjust  the rectangular region with the mouse Drawing method curve point unit surface unit cylinder unit (hidden surface removal) rectangular, cubic unit ray trace a body of rotation (hidden surface removal) a body of rotation ( surface unit) surface point unit line unit only toward one variable direction negative - cross section perpendicular to the x-axis negative - cross section perpendicular to the y-axis negative - cross section perpendicular to the z-axis surface unit hidden surface removal cubic unit ray trace color of solid surface by black, white by the color of dialogue box (appointed color) by brightness by illumination by the color of dialogue box (appointed color( not  to distinguish faces) transparently (distinguishing face) shape of solid surface Triangle -The polygon is subdivided to triangles. Polygon - leave as it is. illumination - in case of drawing  3-dimensional solid,  direction of light and intensive of light is adjustable.           also appointing the effect of shadow,  transparency of light  and the index of refraction and the ratio of reflection. appointing the color background of 'the drawing screen', coordinate axis, internal color of figure section coordinate, coordinate scale - appointment, auto option separately appointing color of character in 2D or 3D screen. appointing line-thickness thickness Graph or figure, coordinate axis, space-frame 8 ~ 14 section coordinate, coordinate scale - appointment, auto option length coordinate scale - appointment, auto option type a dotted line picture collection screen In case of saving pictures by gcg file , the bmp files is saved in the folder which is made below the gcg file..   (Management  becomes convenient.) Making the 'temporary graph memory display window' or  the contents above it  to be seen in a big window function inverse trigonometric function, hyperbolic function, inverse hyperbolic function, sgn, conj Single Integral (indefinite integral) differentiation(derivative), high order differentiation, partial differentiation differential coefficient, high order differential coefficient , partial differential coefficient in the field of complex numbers - included complex operation and function calculation without regard to ciphers - decomposition to prime factors, nPr, nCr,  nHr, n!, +,-,*,/, sqr Matrix - sum, difference, product, scalar  multiple, inverse matrix, determinant, cofactor matrix, transpose matrix, the echelon matrix, the solution  of linear equation, alternating product statistic analysis 