Wikipedia:Reference desk/Archives/Mathematics/2016 November 21

= November 21 =

Cycloid arc length
Can someone take a look at this page here and tell me how does it prove in this sketch that $$\stackrel\frown{PR}=2PQ$$ on the cycloid? It doesn't make much sence to me even for a non-rigorous proof. יהודה שמחה ולדמן (talk) 01:16, 21 November 2016 (UTC)


 * "I don't understand" is not a question that a reference desk is suited to answer. The relevant discussion is on page 8 of that document.  (You could have saved me, and anyone else trying to help, 2 minutes by pointing this out yourself.)  What precisely don't you understand from that argument? --JBL (talk) 20:32, 22 November 2016 (UTC)

History of computer science discipline
Hi all,

I'm interested at the history of computer science as an academic discipline. I know that the world's first computer science degree program began at the University of Cambridge, and that USA's first computer science degree program began at Purdue University.

I would like to know what were the courses and the themes that were studied there at the beginning (1953 in Cambridge, 1962 in Purdue)? I would really like to see some syllabuses, if possible.

Also, of which departments were these program part of? (mathematics department? engineering? something else?) If you can refer me to any further information regarding this issue, I will very appreciate that.

Thank you very much in advance! — Preceding unsigned comment added by 141.226.218.14 (talk) 02:01, 21 November 2016 (UTC)


 * Please don't ask the same question in multiple places. Rojomoke (talk) 06:20, 21 November 2016 (UTC)

Meaning of "algebraically increased by an amount equal to"
What does this mean (PDF file):
 * (a) When p is 101 325 Pa and t is one of the temperatures listed in the attached table then the magnitude of the density in kg.m^-3 is as stated in the table, which is derived from the following formula:
 * d_t = 13 595.08 / {1 + (18 150.36 t + 0.702 09 t^2 + 2.865 5 × 10^-3 t^3 + 2.621 × 10^-6 t^4 ) × 10^-8 }
 * where d_t is the density in kg.m^-3, and t is the temperature in °C;
 * (c) When p differs from 101 325 Pa the magnitude of the density in kg.m^-3 as stated in the attached table or derived therefrom in accordance with the above linear interpolation shall be algebraically increased by an amount equal to 5.47 × 10^-7 (p - 101 325);

Do you multiply d_t by "5.47 × 10^-7 (p - 101 325)", divide by it, or what? 166.186.168.191 (talk) 02:55, 21 November 2016 (UTC)


 * I understand this to mean that you calculate d_t from the table (or directly from the formula if you wish) and then add (or subtract) a correction equal to 5.47 x 10^-7 kg/m^3 times the amount that the pressure is above (or below) 101,325 Pa. So for a pressure of 101,326 Pa you would add a correction of 5.47 x 10^-7 kg/m^3. For a pressure of 101,323 Pa you would subtract a correction of 10.94 x 10^-7 kg/m^3 etc. The correction appears to be a function of pressure only, and not of temperature. Gandalf61 (talk) 11:06, 21 November 2016 (UTC)