# Let ε < 0.

## 09.12.09

### Mathematical limericks, vol. 4

Filed under: Harmonic analysis — Travis @

#### Equations than lend themselves to limericks

Euler’s Equation:

I used to think math was no fun,
‘Cause I couldn’t see how it was done.
Now Euler’s my hero,
For I now see why 0
Equals e pi i + 1.

e raised to the pi times i,
And plus 1 leaves you nought but a sigh.
This fact amazed Euler
That genius toiler,
And still gives us pause, bye the bye.

The Pythagorean Theorem:

A triangle’s sides a, b, c,
With a vertex of 90 degrees,
If that vertext be
‘Tween sides a and b,
The root a-squared plus b-squared is c. [AA]

There are a number of lesser known equations that lend themselves to limerick form:

Equation 1:

A Dozen, a Gross and a Score,
Plus three times the square root of four,
Divided by seven,
Plus five times eleven,
Equals nine squared and not a bit more. [JS]

Equation 2:

Integral v-squared dv
From 1 to the cube root of 3
Times the cosine
Of three pi over 9
Equals log of the cube root of e.

Equation 3:

One over point one-oh-two-three,
When raised to the second degree,
Divided by seven
Then minus eleven
Is approximately equal to e. [AFC]

Equation 4:

Th’integral from e-squared to e
Of 1 over v dot dv,
When raised to the prime
Between five and nine,
Is e to the i pi by 3. [MMB1]

Equation 5:

The integral from naught to pi
Of sine-squared of 2 phi d-phi,
When doubled and then
Not altered again,
Is log (minus 1) over i. [MMB1]

Equation 6:

To find Euler’s Gamma of three,
Integrate to infinity
From zero, dx
x-squared on exp(x),
Or three bang divided by three. [MMB2]

Equation 7:

‘Cause phi-squared less phi, minus 1,
Is exactly equal to none,
The golden mean phi,
Is half of root 5 add on one. [MMB2]

Equation 8:

The square root of minus 2 pi
On th’square root of inverse sine phi;
All that need be done
Is let phi equal one:
It’s twice exp of i pi on i. [AA]

In addition, there are a few figures that lend themselves to limericks:

Figure 1:

If a circle through B, like so,
Has arc AD with center O,
The angle at B,
Wherever B be,
Is half of the angle at O. [MMB1]

Figure 2:

A body with mass m kg
Feels a force of magnitude T.
When its weight t’wards the ground
To speed up at T on m, less g. [AA]