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Hobbyist filmer here. I'd like to make mind-blowing ultra wide-angle images like Terry Gilliam, but in the more economical format of Super 8 mm film. What I do know is that I'm not even remotely looking like Gilliam with any focal length above 18mm...but that's my desired upper length in 35mm only. The focal length to achieve a particular angle of view (which is the thing that makes for the mind-blowing images with wide-angle images) is different with any format and sensor size you use, hence there's articles such as 35 mm equivalent focal length and crop factor. In other words, if you change the format (i. e. size of your film or sensor) but wanna have the same angle of view, you need a different focal length.
Now, I have a chance of acquiring a lens (for a Super8 camera made by the Austrian Eumig brand) which is labeled as ultra wide-angle, according to trade press this lens is guaranteed to be entirely rectilinear (no barrel aka fish-eye distortion, as I don't want this), and its focal length in Super8 is 4mm.
So what I'd like to know is, what's the 35mm equivalent of these 4mm in Super8, according to crop factor? Or in other words: If my desired upper limit is an 18mm focal length in 35mm, what equivalent focal length would that be in Super8?
I guess what might help are the dimensions of the Super8 frame area: 5.97mm horizontal x 4.01mm vertical, compared to 22mm horizontal x 16mm vertical in 35mm.
My second choice would be a 3CCD miniDV with a 1" chip size. What's the equivalent to 18mm there? -- 79.193.41.61 ( talk) 06:50, 18 August 2010 (UTC)
I have always been absolutely terrible at this type of problem. Any hints for making it easier to solve would be appreciated. The basic problem is, given two functions, which is asymptotically greater than the other? In other words, given function f and g, to be asymptotically greater than g, it must be proven that f is O(g). Here is an example and how I solve it (which is surely the most difficult way to solve it):
I solve this by estimating a value for . I will show my steps because I am sure I do not remember the log rules correctly:
Now, if I look at this as , it is obvious that result will be less than 1. Therefore, I claim that g = O(f) and g is asymptotically greater than f. Correct? -- kainaw ™ 20:48, 18 August 2010 (UTC)
Consider a smooth space curve, parametrised by arc length. The Frenet frame {T,N,B} defines a rigid body at each point of the curve. This rigid body is the cube with sides T, N and B. The infinitesimal axis of symmetry of this rigid body is generated by τT + κB where κ is the curvature, and τ is the torsion, of the space curve. This means that infinitesimally the cube is rotating about the line spanned by τT + κB. Can someone show me how to calculate the infinitesimal angular frequency of the cube about this infinitesimal axis of symmetry? — Fly by Night ( talk) 22:55, 18 August 2010 (UTC)
Mathematics desk | ||
---|---|---|
< August 17 | << Jul | August | Sep >> | August 19 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Hobbyist filmer here. I'd like to make mind-blowing ultra wide-angle images like Terry Gilliam, but in the more economical format of Super 8 mm film. What I do know is that I'm not even remotely looking like Gilliam with any focal length above 18mm...but that's my desired upper length in 35mm only. The focal length to achieve a particular angle of view (which is the thing that makes for the mind-blowing images with wide-angle images) is different with any format and sensor size you use, hence there's articles such as 35 mm equivalent focal length and crop factor. In other words, if you change the format (i. e. size of your film or sensor) but wanna have the same angle of view, you need a different focal length.
Now, I have a chance of acquiring a lens (for a Super8 camera made by the Austrian Eumig brand) which is labeled as ultra wide-angle, according to trade press this lens is guaranteed to be entirely rectilinear (no barrel aka fish-eye distortion, as I don't want this), and its focal length in Super8 is 4mm.
So what I'd like to know is, what's the 35mm equivalent of these 4mm in Super8, according to crop factor? Or in other words: If my desired upper limit is an 18mm focal length in 35mm, what equivalent focal length would that be in Super8?
I guess what might help are the dimensions of the Super8 frame area: 5.97mm horizontal x 4.01mm vertical, compared to 22mm horizontal x 16mm vertical in 35mm.
My second choice would be a 3CCD miniDV with a 1" chip size. What's the equivalent to 18mm there? -- 79.193.41.61 ( talk) 06:50, 18 August 2010 (UTC)
I have always been absolutely terrible at this type of problem. Any hints for making it easier to solve would be appreciated. The basic problem is, given two functions, which is asymptotically greater than the other? In other words, given function f and g, to be asymptotically greater than g, it must be proven that f is O(g). Here is an example and how I solve it (which is surely the most difficult way to solve it):
I solve this by estimating a value for . I will show my steps because I am sure I do not remember the log rules correctly:
Now, if I look at this as , it is obvious that result will be less than 1. Therefore, I claim that g = O(f) and g is asymptotically greater than f. Correct? -- kainaw ™ 20:48, 18 August 2010 (UTC)
Consider a smooth space curve, parametrised by arc length. The Frenet frame {T,N,B} defines a rigid body at each point of the curve. This rigid body is the cube with sides T, N and B. The infinitesimal axis of symmetry of this rigid body is generated by τT + κB where κ is the curvature, and τ is the torsion, of the space curve. This means that infinitesimally the cube is rotating about the line spanned by τT + κB. Can someone show me how to calculate the infinitesimal angular frequency of the cube about this infinitesimal axis of symmetry? — Fly by Night ( talk) 22:55, 18 August 2010 (UTC)