http://www.cut-the-knot.org/m/Geometry/TwoIsoscelesFromMiguel.shtml

Finally we met. 

#birdphotography   #naturephotography   #birdsgallery  

a,b,c such that 3≥a≥1≥b,c≥0, a+b+c=3. Prove

abc + 2/(ab+bc+ca) ≥ 5/(aa+bb+cc)

http://www.cut-the-knot.org/arithmetic/algebra/ConstraintInequality2.shtml

#math #inequilities #algebra

Two personalities. I described this photo as "Squeezing in ..." My wife shared it on the facebook with the comment, "Move...make some space for me!"

#birdphotography   #birdsgallery   #naturephotography  

I was used to doing something similar - helping one arm with the other - after a rotation cuff surgery. This may be a rheumatic squirrel to need the same kind of exercise

#naturephotography   #squirrel  

That is a revealing gem concerning devout and, otherwise,  muslim:

The father of Sayed Rizan Farook says his son had an obsessive hatred of Israel that underscored his Islamic radicalism and allegiance to the ideals of Islamic State. He tried to calm down his son by saying "In two years, Israel will be gone...Nobody wants the Jews."

http://live.jpost.com/Middle-East/ISIS-Threat/My-son-was-obsessed-with-Israel-says-father-of-San-Bernadino-shooter-436454

Fill-it-in outline mathematics. Solve in positive integers 20x + 15y = 2015 

http://www.cut-the-knot.org/Outline/Algebra/MilleniumProblem.shtml

x,y,z positive, x ≤ 1, y ≤ 2, x + y + z = 6. Prove (x+1)(y+1)(z+1) ≥ 4xyz.

http://www.cut-the-knot.org/arithmetic/algebra/ConstraintInequality.shtml

The background is a side wall of our library. Were it not for the picture, I would not have realized it is dark.

#birdsgallery   #birdphotography   #naturephotography  

Colors in the fog

#naturephotography   #fallphotography