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Comments on Lecture 2 "Anti-Gravity Slopes"

Comment 1. Road arising the slope illusion

This is a spot on Yashima Drive Way in Kagawa Prefecture, Shikoku Island, Japan. There is a sign saying "Mystery Zone. Be Careful." The left image is a picture taken in the directin of going up this road. The nearer road looks like downhill, but it iis slightly uphill. The road is composed of a slightly uphill slope (the nearer slope) connected to a steeply uphill slope (the farther slope). If we look at this spot from the opposite side (in the direction of going down), we perceive that a downhill slope is connected to an uphill slope, but actually a steeply downhill slope is connected to a slightly downhill slope.

Comment 2. Snow Slopes

These snow slopes were made at Hakkai Sanroku Ski Resort in Minami Uonuma City, Niigata Prefecture, Japan, in March 2019. In this ski resort, they have a white carnival in march every year. We made the snow slopes in connection with this carnival since 2017. It is planned by Ikeda Memorial Art Museum in Minami Uonuma City, and many volunteers join the construction activity. We also planned to make it in 2020, but we gave up because of the lack of snow.

Comment 3. For those who want to construct anti-gravity slopes

The following are books including the diagrams of unfolded surfaces of objects, from which we can construct paper objects including antigravity slopes. In the first five books, the diagrams are perforated, and each part can be separeted easily. In others the diagrams are printed and so we need to make a copy on hard paper for the construction.


Trick Art Object Construction Kit (K. Sugihara, Kinohoshisha Publisher)
It contains four objects, among which "Anti-Gravity Garage Roof" and "Magnet-Like Slopes" belong to the anti-gravity slopes.


Trikc Art Object Construction Kit 2 (K. Sugihara, Kinohoshisha Publisher)
It contains four objects, among which "Anti-Gravity Circular Cylinder" and "Anti-Gravity Cascaded Three Slopes" belong to the anti-gravity slopes.


Trick Art Objject Construction Kit 3 (K. Sugihara, Kinnohoshisha Publisher)@
It contains four objects, among which "Anti-Gravity Loop Slopes" and "Anti-Gravity Dodecahedron" belong to the anti-gravity slopes.


Trick Ojbect Construction annj (K. Sugihara, Nagaoka Shoten Publisher)
It contains unfolded surface diagrams made of plastic, instead of sheets of paper.s. So we can construct plastic objects. Four objects are contained, and three of them belongs to the anti-gravity slopes. They are "Anti-Grafity ZigZag Slope," Magnet-Like Three Slopes" and "Anti-Gravity Four-Sided Roof."


Optical Illusion Trick Kit (K. Sugihara, Gentosha Publisher)
It contains unfolded surfaces of five objects. There is one anti-gravity slope object "Sakasama Slopes," whose structure is the same as the one we made of snow.


The following books contains printed diagrams for illusion objects. You should copy the diagram onto hard sheets of paper for the construction.


Unexpected Strange Objects (K. Sugihara, Seibundo Shinko Sha Publisher)
It contains 20 objects, among which 14 objects are variations of the anti-gravity slopes. The set of two slopes shown at the beginning of the lecture is included.


Trick Papercraft BOOK (K. Sugihara, Shufu To Seikatu Sha Publisher)
It includes "Magnet-Like Slopes."


Mystery World of Impossible Ojbects (K. Sugihara, Seibundo Shinko Sha Publisher)
It includes five objects, among which "Magnet-Loke Slopes" and "Anti-Gravity Round Roof" belong to the anti-gravity slopes.

Comment 4. References on the anti-gravity slopes

K. Sugihara: A characterization of a class of anomalous solids. Interdisciplinary Information Sciences, vol. 11, no. 2 (2005), pp. 149--156.
K. Sugihara: Design of solids for antigravity motion illusion. Computational Geometry: Theory and Applications, vol. 47 (2014), pp. 675-682.