Please be happy & enjoy being alive!

If the edge of the cube be 2, the edges of the *regular tetrahedron* (in the interior) will have length = 2.sqrt(2) & its volume will be 8/3. Now, the *trt* has the same base as a face of the reg. tetrahedron & 1/2 its altitude, so its volume is 4/3. Together:

8/3 (reg. tetrah.) + 4. 4/3 (trt's)= 24/3 = 8 (volume of the cube)

This is *Nordstrand*'s *weird quartic* surface. (Repost of June 4, 2016)

z= 0 > 25(x^2+y^2) +50xy -4=0 > y= -25x +-10.

Please be happy & enjoy being alive, everyone!

[This is respectfully dedicated to the memory of my dearest friend, Ms *Nastasya Lee*, who made me the honor to appreciate my contributions to this community. Thank you.]

The final formulae are:

N= 4.x^3 + 6.x^2 + 4.x + 1= (2.x+1)(2.x^2 + 2.x +1) & the genus:

g= 12. x^3 + 6.x^2 = 6.x^2(2.x+1)

voila! I thank you all for reading this and please be happy you all! New subject in next post...

please be happy everybody & enjoy [autumn] while cold in not too much!

[this was posted the 1st time in the Google-plus "Mathematics community" in Nov 6, 2015]

Feuerbach's theorem (bis)

The so-called *9-point circle* is, according to *Feuerbach's theorem*, tangent to the *inscribed circle* (*10th point*) & to the *3 escribed circles* of the triangle, so it should be called the 13-point circle, at the very least.. (lol) [cf.http://arxiv.org/pdf/1107.1152.pdf ]

Again, please be happy, everyone & enjoy being alive!

Please be happy you all & enjoy being alive!

A very erotic & sensual animation copied from the internet a few days ago. Enjoy & be happy, everyone!

I am an ordinary man, who *lives* & *loves* passionately every moment of his life!...

Joined Feb 2019