Just for fun

What fun or important formulas would you put on a shirt?

June 2, 2018 Just for fun 2 comments ,

Lance got a custom made glow in the dark “math, physics, and chemistry” shirt for his birthday a year or two ago (It was Sofia’s idea, she bought the materials, and I got to play.)

He is clearly unimpressed with the photo op, but I wanted to share this shirt, which includes some of the what I thought were a number of the most interesting or important relationships

  • Gamma function, which generalizes factorial to non-integer values.
    \begin{equation}\label{eqn:formulas:20}
    \Gamma(z + 1) = \int_0^\infty t^z e^{-t} dt.
    \end{equation}
    This formula satisfies \( n! = \Gamma(n + 1) \).

  • Euler’s:
    \begin{equation}\label{eqn:formulas:40}
    e^{n i \theta} = \lr{ \cos\theta + i \sin\theta }^n.
    \end{equation}

  • Schr\”{o}dinger’s equation
    \begin{equation}\label{eqn:formulas:60}
    i \, \hbar \PD{t}{} \ket{\psi} = H \ket{\psi}.
    \end{equation}

  • Taylor series
    \begin{equation}\label{eqn:formulas:80}
    f(x) = \sum_{k = 0}^\infty \frac{f^{(k)}(0)}{k!} x^k.
    \end{equation}

  • Euler-Lagrange equations:
    \begin{equation}\label{eqn:formulas:100}
    \PD{x_i}{\LL} = \frac{d}{dt} \PD{\dot{x}_i}{\LL}.
    \end{equation}
    These formulas can be used to express most dynamics relations. You can think of them as basically being the consequence that physical laws are either inherently greedy or lazy.

  • Stokes’ theorem, in its geoemetric algebra form
    \begin{equation}\label{eqn:formulas:120}
    \oint_{\partial V} d^n \Bx \cdot T = \int_V d^n \Bx \cdot \lr{ \spacegrad \cdot T }.
    \end{equation}

  • Quantum commutator relationships between position and momentum
    \begin{equation}\label{eqn:formulas:140}
    \antisymmetric{X}{P} = i \, \hbar.
    \end{equation}

  • Fourier transform
    \begin{equation}\label{eqn:formulas:160}
    \tilde{f}(\omega) = \int_{-\infty}^\infty f(t) e^{-i \omega t} dt.
    \end{equation}

  • Vector product
    \begin{equation}\label{eqn:formulas:180}
    \Ba \Bb = \Ba \cdot \Bb + \Ba \wedge \Bb.
    \end{equation}
    In geometric algebra the vector product has a dot and wedge product split. In \R{3} you can write this as
    \( \Ba \Bb = \Ba \cdot \Bb + I (\Ba \cross \Bb) \), where \( I = \Be_1 \Be_2 \Be_3 \).

  • Relativisitic energy (Einstein’s)
    \begin{equation}\label{eqn:formulas:200}
    E = \frac{m c^2}{\sqrt{1 – (\Bv/c)^2}}.
    \end{equation}

  • Cauchy contour integral relationships for the nth derivative
    \begin{equation}\label{eqn:formulas:220}
    f^{(n)}(s) = \frac{n!}{2 \pi i} \int_C dz \frac{f(z)}{(z-s)^{n+1}}
    \end{equation}

  • Maxwell’s equations
    \begin{equation}\label{eqn:formulas:240}
    \begin{aligned}
    \partial_\mu F^{\mu\nu} &= J^\nu \\
    \epsilon^{\mu \nu \rho \sigma} \partial_\nu F_{\rho \sigma} &= 0.
    \end{aligned}
    \end{equation}
    I’m partial to the geometric algebra form of Maxwell’s equations \( \grad F = J \), but that wouldn’t have looked as good on the shirt.

  • Dirac equation
    \begin{equation}\label{eqn:formulas:260}
    0 = \lr{ i \gamma^\mu \partial_\mu – m } \psi.
    \end{equation}

If you had to pick a set of important formulas on a tee-shirt, which ones would you pick?

Make a difference, sponsor a warlord — CIA advertisement

November 10, 2014 Just for fun No comments , , , , ,

The Toike Oike, UofT’s engineering newspaper, has reached majestic heights of spoof advertisement in the November issue, with the following advert placed by the CIA

make a difference sponser a warlord, CIA advertisment

The sad thing is that there is so much truth embedded in this bit of parody.

I congratulate the author for most excellent work. Very nice work! Oh, and finding the smiling guy in fatigues with his gun toting buddies in the background was a real nice compositional touch.