Cool math expression with the numbers e, 5, and 0.5
I have discovered a pretty cool mathematical expression:
-5*e^(5arccos((((5^(0.5))*0.5)+0.5)*0.5)*((-5/5)^0.5))
OR
What is neat about this is that:
- Besides arccos’s “-1” (which shouldn’t even be there anyway) and e, the only numbers that appear are 5 and 0.5.
- The number 5 appears 5 times.
- The number 0.5 appears 5 times, counting the square roots as exponents to the power of 0.5.
- It equals 5.
How does it work?
I relied on a few tricks while constructing it.
- e^(pi*i) = -1
an infamous formula - 5arccos((((5^(0.5))*0.5)+0.5)*0.5) = pi
Alex Williams discovered this little gem - Balancing out where the square roots should go, so (-5/5)^0.5) versus (-5)^0.5) / (5^0.5).
I find sharing how math tricks are made does take away the mystery sometimes, but maybe in the future I’ll post one that other people solve.
