Lnewqban's latest activity

I had an overnight revelation about this. It should resonate with any person who has been sensitized to the importance of units. Here it...

Trigonometric proof ##\theta +\varphi=90^{\circ}## Therefore ##\tan\theta=\cot\varphi\implies \tan\theta \tan\varphi=1.##...

Here is how it can be done without Pythagoras or trigonometry. Right triangles ADC and CDB are similar. Therefore...

From the book I gather Descartes starts with line segment we call ##b## then extends it by ##a## which he takes as 1. His goal is to...

@kuruman's construction can also be solved using Pythagoras on the three right angled triangles: $$\begin{eqnarray} h_1^2&=&b^2+h^2\\...

##r^{2}=h^{2}+\left(r-a\right)^{2}\Rightarrow h^{2}=2ar-a^{2}=a\left(2r-a\right)=ab\Rightarrow h=\sqrt{ab}\quad\blacksquare##

In the figure below of a semi-circle, show that ##h=\sqrt{ab}##. In the special case where ##a=1## unit length, then ##h=\sqrt{b}##. A...

Here is a little puzzle from Pierre Berloquin’s book 100 Geometric Games. The goal is to cut the figure once to make two identical...

Is this the third solution you had in mind?

Another solution F is on AC. ##\angle ACD = \pi/4## ##\angle AOD=\pi/2## ##\triangle AEO \equiv \triangle OGD## ##EO=GD## Thus...

Here is my proof. $$r_1^2+(r_1+d)^2=R^2=r_2^2+(r_2-d)^2$$ Solving for ##d##$$d=\frac{r_2^2-r_1^2}{r_2+r_1}=r_2-r_1$$ Therefore...

Have a look at this article about the Cycloid motion of a point on a wheel: https://en.wikipedia.org/wiki/Cycloid...

I only have limited experience riding horses (especially riding them fast or on steep slopes), but in motocross and dirtbike riding, in...

Your shifting forward may have been counterproductive. That action, while in progress, would have created a torque tipping the horse...

I have represented the horse's center of mass with no rigor at all, since I don't know where exactly it may be. What I tried...