Dave Richeson on X: "Euler proved that π/4=arctan(1/2)+arctan(1/3), which can be used for computing digits of π (using the arctangent series). I wondered if I could prove it without using a trig
![trigonometry - What is the value of $\arctan(1/2)+\arctan(1/5)+\arctan(1/8)$? - Mathematics Stack Exchange trigonometry - What is the value of $\arctan(1/2)+\arctan(1/5)+\arctan(1/8)$? - Mathematics Stack Exchange](https://i.stack.imgur.com/jKnbo.png)
trigonometry - What is the value of $\arctan(1/2)+\arctan(1/5)+\arctan(1/8)$? - Mathematics Stack Exchange
I love maths - arctan(1/3)+arctan(1/2)=arctan1...As the total angle made by green and blue angle is nothing but an angle created by diagonal of a square (which is π/4). | Facebook
![Studio della funzione f{{\left({x}\right)}}= \ln{{x}}- \arctan{{\left({x}-{1}\right)}} con commento audio Studio della funzione f{{\left({x}\right)}}= \ln{{x}}- \arctan{{\left({x}-{1}\right)}} con commento audio](https://www.skuola.net/news_foto/2017/09/lnx-arctanx-1.jpg)
Studio della funzione f{{\left({x}\right)}}= \ln{{x}}- \arctan{{\left({x}-{1}\right)}} con commento audio
![The function f (x) = arctan(1/x) − x/(1 + x 2 ) plotted with its real... | Download Scientific Diagram The function f (x) = arctan(1/x) − x/(1 + x 2 ) plotted with its real... | Download Scientific Diagram](https://www.researchgate.net/publication/257341129/figure/fig2/AS:670006954188813@1536753514531/The-function-f-x-arctan1-x-x-1-x-2-plotted-with-its-real-entire-majorant-and.png)