Henry Segerman - Stereographic

Henry Segerman is an Associate Professor in the Department of Mathematics at Oklahoma State University. In addition to his research in three-dimensional geometry and topology, he is also a mathematical artist, working primarily in the medium of 3D printing, with other interests in virtual reality and spherical video.

In Henry's works, I got interested in his Stereographic projection projects. Stereographic projection is a map from the sphere to the plane. Imagine straight lines going from the north pole of the sphere down onto the plane. Each line hits the sphere at one point and the plane in one point. Stereographic projection maps that point on the sphere to the point on the plane. 

So if you put a light source at the north pole of this sculpture, the rays of light effectively do stereographic projection. The curves on the sphere cast shadows, mapping them to a straight line grid on the plane.

Grid (stereographic projection)

Dual circles

732_Triangle tiling

632_Triagle tiling

442_Triangle tiling

532_Triangle tiling

Honeycomb

http://www.segerman.org/ 

https://www.amazon.com/Visualizing-Mathematics-Printing-Henry-Segerman/dp/142142035X

PointCloud

Zionskirche in 3D from Steffen Sommer on Vimeo.

https://constructible.trimble.com/construction-industry/what-is-a-point-cloud

Akira (1988 film)_Interesting visual effect of the trace of movement

Akira (Japanese: アキラ Hepburn: Akira) is a 1988 Japanese animated post-apocalyptic cyberpunk film directed by Katsuhiro Otomo, produced by Ryōhei Suzuki and Shunzō Katō, and written by Otomo and Izo Hashimoto, based on Otomo's manga of the same name. The film had a production budget of ¥1.1 billion^[1] ($9 million),^[2] making it the most expensive anime film of its time.^[4]

Water Clock Korea 'Jagyeongnu'

The water clock worked by having water poured into the largest bronze vessel which flowed into the smaller vessels which then flowed into the long water tanks. When the water level rose to the appropriate level, a floating rod touched a lever device which caused a ball to roll and hit another ball at the other end. The rolling ball would trigger the gong, bell, drum, and even a wooden puppet which marked the hour with a placard.

Olafur Eliasson:The illusion of stopped movement and time--within an artwork that incorporates actual movement and time

In a darkened room, there is a pool of water on the floor and water dripping from the ceiling into the pool. This is what you know when you step into the room. But it is lit only with strobe light, so all you have are flashes of information as to what you are seeing. The strobe light freezes the movement of the water drops, in an endless variation. It is like seeing time stopped. The effect is mesmerizing and magical. Along with the slight coolness of the room and the scent of cool fresh water, it becomes a transcendent moment.

Definition of 'Hertz'

The hertz is defined as one cycle per second. The International Committee for Weights and Measures defined the second as "the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom"^[2][3] and then adds: "It follows that the hyperfine splitting in the ground state of the caesium 133 atom is exactly 9 192 631 770 hertz, ν(hfs Cs) = 9 192 631 770 Hz." The dimension of the unit hertz is 1/time (1/T). Expressed in base SI units it is 1/second (1/s).

In English, "hertz" is also used as the plural form.^[4] As an SI unit, Hz can be prefixed; commonly used multiples are kHz (kilohertz, 10³ Hz), MHz (megahertz, 10⁶ Hz), GHz (gigahertz, 10⁹ Hz) and THz (terahertz, 10¹² Hz). One hertz simply means "one cycle per second" (typically that which is being counted is a complete cycle); 100 Hz means "one hundred cycles per second", and so on. The unit may be applied to any periodic event—for example, a clock might be said to tick at 1 Hz, or a human heart might be said to beat at 1.2 Hz. The occurrence rate of aperiodic or stochastic events is expressed in reciprocal second or inverse second (1/s or s⁻¹) in general or, in the specific case of radioactive decay, in becquerels.^[5] Whereas 1 Hz is 1 cycle per second, 1 Bq is 1 aperiodic radionuclide event per second.

헤르츠 (hertz, 기호: ㎐, 문화어: 헤르쯔)는 SI 단위계의 주파수 단위이다. 이 이름은 전자기학 분야에서 업적을 남긴 독일 물리학자 하인리히 루돌프 헤르츠(Heinrich Rudolf Hertz)를 기리기 위한 것이다.

1 ㎐는 SI 기본 단위로 표현하면 1 s${\displaystyle ^{-1}}$이다. 1 Hz는 “1초에 한 번”을 의미한다. 즉 100 Hz는 1초에 100번을 반복 혹은 진동함을 뜻한다. 이 단위는 모든 주기적으로 반복되는 것에 쓰일 수 있다. 매우 간단한 예로 정확히 맞는 시계의 초침은 1 Hz로 똑딱거린다.

우리가 일상생활에서 주로 접하는 경우는 라디오나 텔레비전 방송의 주파수, 컴퓨터 CPU의 클럭 주파수 등이다.

Electromagnetic radiation is often described by its frequency—the number of oscillations of the perpendicular electric and magnetic fields per second—expressed in hertz.

Radio frequency radiation is usually measured in kilohertz (kHz), megahertz (MHz), or gigahertz (GHz). Light is electromagnetic radiation that is even higher in frequency, and has frequencies in the range of tens (infrared) to thousands (ultraviolet) of terahertz. Electromagnetic radiation with frequencies in the low terahertz range (intermediate between those of the highest normally usable radio frequencies and long-wave infrared light) is often called terahertz radiation. Even higher frequencies exist, such as that of gamma rays, which can be measured in exahertz (EHz). (For historical reasons, the frequencies of light and higher frequency electromagnetic radiation are more commonly specified in terms of their wavelengths or photon energies.

Definition of 'Chronophotography'

Chronophotography is an antique photographic technique from the Victorian era (beginning about 1867–68), which captures movement in several frames of print. These prints can be subsequently arranged either like animation cels or layered in a single frame. It is a predecessor to cinematography and moving film, involving a series of different cameras, originally created and used for the scientific study of movement.

Chronophotography is defined as "a set of photographs of a moving object, taken for the purpose of recording and exhibiting successive phases of motion".^[2] The term chronophotography was coined by French physiologist Étienne-Jules Marey to describe photographs of movement from which measurements could be taken and motion could be studied. It is derived from the Greek word χρόνος chrónos ("time") combined with photography.