Mathematical Science Developing from Figures (Global Focus on Knowledge)
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Polyhedra
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#1 Euler’s Formula and The Regular Polyhedra
Probably you feel that you know very well about POLYHEDRA, surrounded by a plenty of them in your daily life. Surprisingly enough, though, there are quite a few open problems on them, which are stated in purely elementary words so that even small children can understand what those problems mean. These three lectures are designed as a rather informal or casual introduction to the subjects. Indeed,…
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Available
Audio-Only
Listening
#2 Rigidity and Deformation of Polyhedra
Probably you feel that you know very well about POLYHEDRA, surrounded by a plenty of them in your daily life. Surprisingly enough, though, there are quite a few open problems on them, which are stated in purely elementary words so that even small children can understand what those problems mean. These three lectures are designed as a rather informal or casual introduction to the subjects. Indeed,…
Available
Audio-Only
Listening
Available
Audio-Only
Listening
#3 Unsolved Problems on Polyhedra
Probably you feel that you know very well about POLYHEDRA, surrounded by a plenty of them in your daily life. Surprisingly enough, though, there are quite a few open problems on them, which are stated in purely elementary words so that even small children can understand what those problems mean. These three lectures are designed as a rather informal or casual introduction to the subjects. Indeed,…
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Mathematical Principles and Computations of Origami
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#4 Computational Origami and Shapes
Origami, the traditional Japanese art of folding paper, has now become a hot research theme studied worldwide across various fields such as art, mathematics, computer science, material science, life science, structural engineering, robotics, and architecture. These lectures will introduce mathematical principles and computational techniques of origami that bridge these interdisciplinary themes, i…
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Available
Audio-Only
Listening
#5 Mechanisms of Origami
Origami, the traditional Japanese art of folding paper, has now become a hot research theme studied worldwide across various fields such as art, mathematics, computer science, material science, life science, structural engineering, robotics, and architecture. These lectures will introduce mathematical principles and computational techniques of origami that bridge these interdisciplinary themes, i…
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Periodicity and Symmetry
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#6 Recognizing Symmetry, Recognizing Periodicity
We can discover many symmetric figures in everyday life and in nature. Numerous artworks possess beautiful symmetry as well. Periodicity can be observed in a multitude of infinitely expanding figures. We can describe symmetry and periodicity in the space by mathematics. Then we can classify the symmetry or the periodicity into finitely many groups.
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Listening
Available
Audio-Only
Listening
#7 Understanding Space with Rotations and Translations
We can discover many symmetric figures in everyday life and in nature. Numerous artworks possess beautiful symmetry as well. Periodicity can be observed in a multitude of infinitely expanding figures. We can describe symmetry and periodicity in the space by mathematics. Then we can classify the symmetry or the periodicity into finitely many groups.
Available
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Listening
Available
Audio-Only
Listening
#8 Polyhedra That Fill the Space
We can discover many symmetric figures in everyday life and in nature. Numerous artworks possess beautiful symmetry as well. Periodicity can be observed in a multitude of infinitely expanding figures. We can describe symmetry and periodicity in the space by mathematics. Then we can classify the symmetry or the periodicity into finitely many groups.
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Looking at the Shape of Space from Four-Dimensional Polytopes
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#11 Let's Look at Four-Dimensional Figures
We can project three-dimensional figures on a plane, but how can we visualize four-dimensional figures? In these lectures, we will first consider regular polyhedra in the four-dimensional space. Second, the lecture will explain the history of space recognition from Euclid’s Elements to the discovery of non-Euclidean geometry and Riemannian geometry. Furthermore, the lecture will describe ap…
Available
Audio-Only
Listening
Available
Audio-Only
Listening
#12 What Does It Mean That Space Is Curved?
We can project three-dimensional figures on a plane, but how can we visualize four-dimensional figures? In these lectures, we will first consider regular polyhedra in the four-dimensional space. Second, the lecture will explain the history of space recognition from Euclid’s Elements to the discovery of non-Euclidean geometry and Riemannian geometry. Furthermore, the lecture will describe ap…
Available
Audio-Only
Listening
Available
Audio-Only
Listening
#13 Topology of the Universe
We can project three-dimensional figures on a plane, but how can we visualize four-dimensional figures? In these lectures, we will first consider regular polyhedra in the four-dimensional space. Second, the lecture will explain the history of space recognition from Euclid’s Elements to the discovery of non-Euclidean geometry and Riemannian geometry. Furthermore, the lecture will describe ap…
Available
Audio-Only
Listening
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