Today is a great day. We get to celebrate one of the best numbers in existence: π. π plays a role in many mathematical and scientific applications. Some examples include:
Area of a Circle = π * radius^2
Area of an Ellipse = π * length of semimajor axis * length of semiminor axis
The functions sin x, cos x, and tan x each have a period of π.
Euler's Formula: e^(i*π) + 1 = 0
Definite integral involving π:
∫(e^(a*x^2) dx, 0, infinity) = 0.5 * √(π/a)
1 + 1/3 + 1/5 + 1/7 + ... = sum of the fractions of 1/odd integers = π/4
(Convergence might be slow)
Γ(1/2) = √π. (Gamma of 1/2)
Probability: Area under the Normal Curve:
1/√(2 π) * ∫(e^(x^2/2))
Angular Velocity, general: ω = 2 π f, where f is frequency
Conversion between radians and degrees:
Angle in Radians = Angle in Degrees * π/180
Optics: Double Split Interference  Intensity at an Angle:
I = 4 * I_0 * cos( π * d * sin θ / λ )^2
Also today is Albert Einstein's birthday (March 14). He is primarily responsible for the Theory of Relativity and E = mc^2. I am going to give myself a refresher course.
Here is some information about the Theory of Relativity:
http://en.wikipedia.org/wiki/Theory_of_relativity
This blog is property of Edward Shore. 2014
A blog is that is all about mathematics and calculators, two of my passions in life.
Friday, March 14, 2014
Happy π Day! Happy Birthday Albert Einstein!
Subscribe to:
Post Comments (Atom)
Expanding Linear Regression
Expanding Linear Regression Introduction – Linear Regression All scientific calculators that have twovariable dimensions has cu...

Casio fx991EX Classwiz Review Casio FX991EX The next incarnation of the fx991 line of Casio calculators is the fx991 EX. ...

TI36X Pro Review This is a review of the TI36X Pro Calculator by Texas Instruments. History Originally, this was the TI30X Pro that w...

One of the missing features of the TI82/83/84 family is the ability to convert between bases. Here are two programs in TIBasic to help...
No comments:
Post a Comment