## Lens – Do mounting adapters change apparent focal lengths of lenses?

I have a Sony A6500 APS-C camera using a Sony 55-210mm lens.

I wanted more scope and so I rented a Sigma 18-300mm lens to use with a Sigma MC11 adapter.

By testing this configuration, I get an identical picture with the Sony lens at 200mm and the Sigma at 300mm.

The Sigma lens setting on 200mm gives a wider-angle picture compared to the Sony 200mm lens. It seems that the cropping factor of 1.5 is revised when using an adapter.

Why does the Sigma lens seem to have different focal lengths for the Sony lens? Is this caused by the adapter?

## List Handling – What is the best way to join tables that have different lengths on the same column values ​​that exist in both tables?

I think my problem is pretty simple, and in SQL it would be trivial. I have two tables

``````TableOne = {{a, x1}, {b, x2}, {c, x3}};
TableTwo = {{a, y1}, {c, y2} , {a, y3}, {a, y4}, {b, y5}, {c,y6}, {c, y7}}
``````

I want to be able to join these two tables where the values ​​in column 1 in both tables match such as:

``````DesiredResult =  {{a, x1, a, y1}, {c, x3 , c, y2} , {a, x1, a, y3}, {a, x1, a, y4}, {b, x2, b, y5}, {c, x3, c, y6}, {c, x3, c, y7}}
``````

I've tried with both `Select[]` statements inside a `Table[]` the structure and also examined `JoinAcross[]` but have not managed to get the desire effect. In SQL, it would be simple, something like:

``````SELECT Col1.Table1, Col2.Table1, Col1.Table2, Col2.Table2,  FROM table2 INNER JOIN table1 ON Col1.Table1  = Col1.Table2
``````

Or something similar.

## Geometry – A curious relationship between the angles and the lengths of a tetrahedron's edges

Consider a Euclidean tetrahedron with edge lengths edge lengths $$l_ {12}, l_ {13}, l_ {14}, l_ {23}, l_ {24}, l_ {34}$$ and dihedral angles $$alpha_ {12}, alpha_ {13}, alpha_ {14}, alpha_ {23}, alpha_ {24}, alpha_ {34}.$$
Consider solid angles
$$begin {split} & Omega_1 = alpha_ {12} + alpha_ {13} + alpha_ {14} – pi \ & Omega_2 = alpha_ {12} + alpha_ {23} + alpha_ {24} – pi \ & Omega_3 = alpha_ {13} + alpha_ {23} + alpha_ {34} – pi \ & Omega_4 = alpha_ {14} + alpha_ {24} + alpha_ {34} – pi \ end {split}$$
and perimeters of faces
$$begin {split} & P_1 = l_ {23} + l_ {34} + l_ {24} \ & P_2 = l_ {14} + l_ {24} + l_ {12} \ & P_3 = l_ {13} + l_ {34} + l_ {14} \ & P_4 = l_ {12} + l_ {23} + l_ {13}. \ end {split}$$
Then, the following cross ratios are equal:
$$[e^{iOmega_1}, e^{iOmega_2}, e^{iOmega_3}, e^{iOmega_4}]=[P_1, P_2, P_3, P_4].$$
Question: Is this known? I have found a proof of this affirmation (to be published soon), but it implies a rather delicate algebraic geometry. It will be very interesting for me to see a more basic approach.

## google sheets – Using IMPORTRANGE to juxtapose lists of varying lengths

Suppose I have two Google sheets, Doc1 and Doc2, both of which have only one sheet with two lists with the same schema, say two columns Name and Age. The number of entries in the lists is unknown, but if it makes the task easier, we can assume that they have at most 5 entries:

I want to bring the two lists together and display them in a third "Summary" document, one after the other. I can show them using these formulas, in the Summary cells `A1` and `A6`, respectively:

``````= IMPORTRANGE ("1cLqgopAWG ...", "Sheet1! A1: B5")
= IMPORTRANGE ("1564EXoW-s ...", "Sheet1! A1: B5")
``````

However, this leaves a boring variable number of blank lines between the two:

while I would like to show them one directly above the other, as if (manually copied values ​​here to show what I want):

If I try to use `IMPORTRANGE` in two contiguous rows (i.e. `A1` and `A2`), I have a `#REF!` error ("The result of the array was not expanded because it would overwrite the data in A2."):

Is it possible to achieve what I want?
(Bonus points to remove the constraint on the maximum number of items.)

## Telephoto – Selecting a tripod for use with very long focal lengths

I play with very long focal lengths with a Kenko 3x teleconverter. I had a hard time getting sharp pictures and I think camera shake is an important part of that.

Since I plan to buy a tripod to lock the objects.

What should I look for in a tripod in this context?
I'm currently using the 100-300 f4 sigma and a 5d mark ii canon, but is also planning to get a 150-600 mm zoom and the MTO-1000 mirror lens, so I wish work with a tripod.

I've heard that a heavy tripod is recommended in this context, is this correct and if so, how heavy is it?

Looking at the web, I found the Genesis A3 Tripod http://www.genesisgear.pl/en/kits/75-genesis-a3-kit-en that looked promising. Am I on the right track with this?

## google sheets – Including insignificant zeros at the beginning of numbers of varying lengths

I'm trying to digitize numbers in Google spreadsheets, but some of those numbers start with a zero. Currently, my spreadsheet automatically removes zeros, but I want to keep them. The plain text will allow me to do this, but I can not format it in plain text and format my custom number at the same time. My current numeric formatting is "asterisk"0"asterisk"… it's essential because I have to start and end all the numbers in the sheet with an asterisk." All solutions consulted online recommend adding more zeros to my formatting, such as "asterisk"000000"asterisk"… but all the numbers in my spreadsheet do not include zeros at the beginning, I do not want to add zeros at the beginning of every number in the spreadsheet, I just want to keep them at the beginning of For example, some of the numbers I scan in the sheet should look like "12345", while others should look like "012345" I do not want to add zeros, just keep only existing zeros that I scan into the sheet.

## r – Error in model.frame.default () variable lengths differ (found for '(weight)')

I am new to R and I am using multinomial logistic regression in R, but this continues to display the error:

``````library (nnet)
train <-multinom (Crime_code ~ Year + Month + Day + Weekday + Time + Time + Area + District + Longitude + Latitude, data = train, size = 11, max = 1700, weight = 1700)
## Error in model.frame.default (formula = Crime_code ~ Year + Month + Day +: variable lengths differ (found for & # 39; (weight) & # 39;)
summary (train)
## Error in the object[[i]]: the object of type "close" is not under-usable
``````

Here is the data structure:

``````str (train)
& # 39; data.frame & # 39 ;: 1760097 obs. of 12 variables:
\$ DR: int 120215758 160512269 112104909 121523303 162107991
161407795 180409993 130911557 120405961 160221815 ...
\$ Year: int 2012 2015 2011 2012 2016 2016 2018 2013 2011 2016 ...
\$ Month: int 8 9 1 12 2 2 5 6 9 12 ...
\$ Day: int 5 1 18 9 24 24 18 3 1 12 ...
\$ Week: int 6 1 1 6 2 2 4 0 3 0 ...
\$ Time: int 2345 800 5 1200 1630 910 1910 1240 2000 1800 ...
\$ Time: int 23 8 0 12 16 9 19 12 12 18 18 ...
\$ Zone: int 2 5 21 15 21 14 4 9 4 2 ...
\$ District: int 201 513 2105 1583 2185 1453 489 964 416 233 ...
\$ Longitude: num -118 -118 -119 -118 -119 ...
\$ Latitude: num 34.1 33.8 34.2 34.1 34.2 ...
Crime_code: int 624 354 220 745 310 624 626 624 230 420 ...
``````