Whitney brothers (John and James) who are said to be the founder of computer movies. They developed abstract movies. James, especially, who was influenced by Oriental thought, developed Yantra in 1955, after endeavoring to create a movie by manipulating a vast amount of shining particles. John collaborated in his brother's researches and tried to develop a more practical device to express figures. He invented an apparatus that made motion pictures of Lissajous's figure in 1957, and the motion graphic system using the analogue computer in 1958. This study delves into the Whitney brothers' methods of creation, distinctive features of their works, the development of the computer and their motive for using it for creative purposes, and their contribution to the progress in Graphics.

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We define the inner (+) and the outer (-) part of the Cartesian Oval as mr₁±nr₂ = kc on bipolar coordinates.
We can consider on Minor axis (asymmetry axis) of the inner part of the Oval, and can define Major axis (asymmetry axis) of the outer part of the Oval. This major axis is a segment which connects the middle point O of symmetry axis and the point Fp on the oval, which is at the longest distance from the point O. Then, the length of major axis is ao (1 + e_L e_R) ^1/2 (where ao is a half of the length of the symmetry-axis, e_L, e_R are left and right eccentricity of the Oval, respectively.) And, we can say that Cardioid is the special case of Cartesian Oval. In this case, e_L and e_R are equal to 1 and the length of the major axis is ao 2^1/2.
Moreover, we have found the following Lemma. [Lemma] Let bi be the length of Minor axis of the inner part of the Oval, let ai and ao be the half length of symmetry-axis of the inner and outer part, respectively. Let bo be the length of the Major axis of the outer part. Then, the following invariant holds. (bi/ai) ²+ (bo/ao) ²=2

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CAD faculties were used for the generation of triangles from their three angle-bisectors, with their lengths only given. At this time we account for its theoretical basis, attempts of example drawing in point and measurement on accuracy of those solutions. Relatedly, a new method is introduced for executing on the CAD screen the arithmetic four rules used in the current geometric construction. And, as to any side and angle-bisector of an isosceles triangle, an approximately relationship between both their lengths is provided in equation form. The accuracy in the present onscreen drawing solution has proved to be within 0.04 and 0.4% respectively in constructing isosceles triangles and in using the above equation. How to improve such accuracy and extendedly apply our system to scalene triangles are left for further consideration.

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Graphic education based on descriptive geometry is analyzed on following three aspects, i.e., 1) psychological refusal, 2) lack of direct relations between graphic education and practical design process, and 3) obstructions of creative design education. The conclusions are as follows.1) On psychological refusal we have to adapt the past education as a negative inheritance sincerely. We must respond in the education from now on. 2) On the lack of relations between graphic education and practical design process we must rethink relations between graphic representation and design. 3) On obstructions of creative design education we must recognize descriptive geometry as a particular way of thinking 3 dimensional objects. We should introduce plural views into graphic education.

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When students study a drawing, they don't have a time to understand directions of the drafting tools . On the other hand, effective use of computers is becoming indispensable, and yet remains insufficient. The author seeks to identify the relationship between drawing and graphical analysis that is inherent in the drawing process.
If the problem is different, students should draw newly a figure. In that case, a different problem can be easily drawn by programming an analytical result to the computer.
The author prepared the print, in which an analytical process was explained in detail, to help students understand. And an analytical result could also have been displayed on a personal computer.
As a result, it was necessary to think about the range of applications of the analytical expression.

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