Measurement of solid angles

1965 ◽  
Vol 8 (12) ◽  
pp. 1179-1180
Author(s):  
A. V. Teplov
Keyword(s):  
Solid Angles

Dimensions of plane and solid angles and their units in the International System of Units (SI)

2020 ◽  
pp. 26-32
Author(s):  
M. I. Kalinin ◽  
L. K. Isaev ◽  
F. V. Bulygin
Keyword(s):  
Solid Angle ◽  
International System ◽  
International Committee ◽  
Plane Angle ◽  
Arc Length ◽  
Weights And Measures ◽  
International System Of Units ◽  
System Of Units ◽  
In Series ◽  
Solid Angles

The situation that has developed in the International System of Units (SI) as a result of adopting the recommendation of the International Committee of Weights and Measures (CIPM) in 1980, which proposed to consider plane and solid angles as dimensionless derived quantities, is analyzed. It is shown that the basis for such a solution was a misunderstanding of the mathematical formula relating the arc length of a circle with its radius and corresponding central angle, as well as of the expansions of trigonometric functions in series. From the analysis presented in the article, it follows that a plane angle does not depend on any of the SI quantities and should be assigned to the base quantities, and its unit, the radian, should be added to the base SI units. A solid angle, in this case, turns out to be a derived quantity of a plane angle. Its unit, the steradian, is a coherent derived unit equal to the square radian.

scholarly journals GAMMA-RADIATION SPECTRA OF 1200 MeV ELECTRONS IN THICK BERYLLIUM, SILICON AND TUNGSTEN SINGLE CRYSTALS

2019 ◽  
pp. 86-93
Author(s):  
G. L. Bochek ◽  
O. S. Deiev ◽  
V. I. Kulibaba ◽  
N. I. Maslov ◽  
V. D. Ovchinnik ◽  
...  
Keyword(s):  
Gamma Radiation ◽  
Single Crystals ◽  
Angular Distributions ◽  
Γ Radiation ◽  
Radiation Spectra ◽  
Solid Angles ◽  
Crystallographic Axes ◽  
And Tungsten

Gamma radiation spectra of 1200 MeV electrons from the single crystals of the beryllium 1.2 mm thick, silicon 1.5 mm and 15 mm thick and tungsten 1.18 mm thick along of the crystallographic axes were measured. Also spectral-angular distributions of gamma radiation from the silicon single crystals 1.5 mm thick along of the crystallographic axes < 100 >, < 110 > and < 111 > were measured. On the basis of these measurements the γ-radiation spectra for the different solid angles up to 6.97 × 10−6 sr were obtained.

On the Measure of Solid Angles

1990 ◽  
Vol 63 (3) ◽  
pp. 184 ◽  
Author(s):  
Folke Eriksson
Keyword(s):  
Solid Angles

Reply by author to Dr. LaFehr

Geophysics ◽  
1977 ◽  
Vol 42 (4) ◽  
pp. 877-877
Author(s):  
Shri Krishna Singh
Keyword(s):  
Closed Form ◽  
Solid Angle ◽  
Short Note ◽  
Circular Disc ◽  
Closed Form Expression ◽  
Gravitational Attraction ◽  
Form Expression ◽  
Practical Usefulness ◽  
Solid Angles ◽  
Classic Paper

It is difficult to include all references when dealing with a subject so well studied as the gravitational attraction of a circular disc. Although the practical usefulness of Nettleton’s paper can not be denied by anyone, it nevertheless gives no details (except for some references) of the computation of solid angles subtended by a disc from which his graphs (Geophysics, 1942, Figure 4) result. My short note deals with (in what I consider an easy way of) obtaining a closed form expression for the solid angle. For applications of the result the reader would do well to look up Nettleton’s classic paper.

Viewing the World from Different Angles: Plato’s Timaeus 54E-55A

Apeiron ◽  
2013 ◽  
Vol 46 (3) ◽  
pp. 244-269
Author(s):  
Ernesto Paparazzo
Keyword(s):  
Present Article ◽  
Solid Angle ◽  
Alternative Interpretation ◽  
Plane Geometry ◽  
A Value ◽  
Solid Geometry ◽  
The World ◽  
Euclid’S Elements ◽  
Solid Angles ◽  
The Universe

Abstract The present article investigates a passage of the Timaeus in which Plato describes the construction of the pyramid. Scholars traditionally interpreted it as involving that the solid angle at the vertex of the pyramid is equal, or nearly so, to 180°, a value which they took to be that of the most obtuse of plane angles. I argue that this interpretation is not warranted, because it conflicts with both the geometrical principles which Plato in all probability knew and the context of the Timaeus. As well as recalling the definitions and properties of plane angles and solid angles in Euclid’s Elements, I offer an alternative interpretation, which in my opinion improves the comprehension of the passage, and makes it consistent with both the immediate and wider context of the Timaeus. I suggest that the passage marks a transition from plane geometry to solid geometry within Plato’s account of the universe.

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