This paper analyses the plates of axonometry inserted in“Architectural Fantasy” that is one of the most famous books by Chernikhov, who is called ’Piranesi of USSR’ . Analysis is on following three aspects, a) the composition of the book, b) the intersected angle of three axonometric axes, c) the ratios of axonometric projection. The conclusion is as follows. 1) Both axonometry and perspective are used. 2) Other axonometric drawings than cavalier projection, military projection and isometric projection are used. 3) There are differences between ratios calculated from intersected angles of three axes and those calculated from the projection of circles. So we can point out that in such cases he used the ratio along three axes independent from the intersected angles of axonometric axes.

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There is a task that a student discovers a route which slope is equal on a topographic map. We analyzed factors that university freshmen generated incorrect answers of this task. The results are as follows. First, there were freshmen who were not able to reproduce the procedures of problem solving of the task which we taught. They began to make new procedures, and generated incorrect answer. Second, freshmen were able to perform procedures of the problem solving which we taught. But, they used incorrect knowledge with this problem solving processes, and generated incorrect answer. Third, the incorrect knowledge was the idea that true length of topography was just represented on a topographic map and this concept was different from the principle of projection. It is difficult that usual instruction of engineering graphics remedies this students' misconception.

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This research takes up Lissajous's device invented by Lissajous and had a great influence on Laposky's Graphics the latter half of the 20th century, as well as Braun's invention of the oscilloscope at the end of the 19th century, which contributed to Laposky' Graphics up till 1950.
Then I introduce the technique to express waves and Lissajous figures with the oscilloscope, Burnett's pattern designs, and the application to abstract films by McLaren and pendulum photos. It also describes their influence on later day Laposky's Graphics.

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[in Japanese]

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