# Sample Halloween Math halloweenexample

Sample Halloween Math

A. U. Thor

January 6, 2017

A reduction my students are likely to make:

sin x

s

The same reduction as an in-line formula:

Now with limits:

n

i=1

= x in

sin x

s

i-th magic term

2 i -th wizardry

= x in.

n

And repeated in-line:

i=1 x iy i .

The bold math version is honored:

〈 〉

something terribly

= 0

complicated

Compare it with normal math:

〈 〉

something terribly

= 0

complicated

In-line math comparison: f(x) versus f(x).

There is also a left-facing witch:

And here is the in-line version:

Test for \dots:

sin x

s

sin x

s

= x in

= x in.

n 1

i 1 =1

· · ·

n p

i p=1

i 1 -th magic factor

2 i 1

-th wizardry

· · ·

i p -th magic factor

2 ip -th wizardry

And repeated in-line: · · ·

n

i=1 x iy i .

1

Now the pumpkins. First the bold math version::

Then the normal one:

m⊕

h=1

m⊕

h=1

n

k=1

n

k=1

P h,k

P h,k

n

In-line math comparison:

i=1 P i ≠ ⊕ n

i=1 P i versus

Close test: ⊕⊕ . And against the pumpkins:

m⊕ n

In-line, but with \limits: P h,k .

Binary: x

h=1 k=1

y ≠ x ⊕ y. And in display:

a

x y

x ⊕ y ⊗ b

Close test: ⊕⊕. And with the pumpkins too:

In general,

n

⊕⊕.

n

i=1 P i ≠ ⊕ n

⊕⊕ i=1 P i.

.

The same in bold:

i=1

n

i=1

P i = P 1 · · · P n

P i = P 1 · · · P n

Other styles: x y , exponent Z , subscript W 2 x y, double script 2 t x y .

sin

Clouds. A hypothetical identity: 2 x+cos 2 x

= . Now the same identity

set in display:

cos 2 x

sin 2 x + cos 2 x

=

cos 2 x

Now in smaller size: sin x+cos x = 1.

Specular clouds, bold. . .

. . . and in normal math.

←→

←→

In-line math comparison: ↔ versus ↔ . Abutting: .

2

Ghosts: . Now with letters: H H h ab f wxy , and

also 2 3 + 5 2 − 3 i = 12 4 j. Then, what about x 2 and z +1 = z 2 + z ?

In subscripts:

F +2 = F +1 + F

F +2 = F +1 + F

Another test: | | | | | | | | . We should also try this: .

Extensible arrows:

A

A

A

A

x 1 +···+x n x+z

∋−−−−−− B ∋−−− C ∋−− D

a⋆f(t)

x 1 +···+x n x+z

∋−−−−−− B ∋−−− C ∋−− D

a⋆f(t)

x 1 +···+x n x+z

−−−−−−∈ B −−−∈ C −−∈ D

a⋆f(t)

x 1 +···+x n x+z

−−−−−−∈ B −−−∈ C −−∈ D

a⋆f(t)

And ∋−−−−−−−−−−−−−

x 1 + · · · + x n = 0 versus ∋−−−−−−−−−−−−−

x 1 + · · · + x n = 0; or −−−−−−−−−−−−−∈

x 1 + · · · + x n = 0 versus

−−−−−−−−−−−−−∈

x 1 + · · · + x n = 0.

Hovering ghosts: x 1 + · · · + x n = 0. You might wonder whether there is

enough space left for the swishing ghost; let’s try again: (x 1 + · · · + x n )y = 0.

As you can see, there is enough room. Lorem ipsum dolor sit amet consectetur

too.

A x 1+···+x n

a⋆f(t)

B x+z C D

A

x 1+···+x n

a⋆f(t)

B x+z C D

Another hovering ghost: x 1 + · · · + x n = 0.. Lorem ipsum dolor sit amet

consectetur adipisci elit. Ulla rutrum, vel sivi sit anismus oret, rubi sitiunt

silvae. Let’s see how it looks like when the ghost hovers on a taller formula,

as in H 1 ⊕ · · · ⊕ H k . Mmmh, it’s suboptimal, to say the least. 1

Under “arrow-like” symbols: x 1 + · · · + x n = 0 and x + y + z. There are

x 1 + · · · + x n = 0 and x + y + z as well.

−−−−−−−−−−−−−∈

∋−−−−−−−−−

1 We’d better try y 1 + · · · + y n , too; well, this one looks good!

3

A comparison between the “standard” and the “script-style” over/under

extensible arrows:

−−−−−−−−→

f 1 + · · · + f n ≠ −−−−−−−−−−−−→

f 1 + · · · + f n

←−−−−−−−−

f 1 + · · · + f n ≠ ←−−−−−−−−−−−−

f 1 + · · · + f n

←−−−−−−−→

f 1 + · · · + f n ≠ ←−−−−−−−−−−−→

f 1 + · · · + f n

f 1 + · · · + f n

−−−−−−−−→ ≠ f 1 + · · · + f n

−−−−−−−−−−−−→

f 1 + · · · + f n

←−−−−−−−− ≠ f 1 + · · · + f n

←−−−−−−−−−−−−

f 1 + · · · + f n

←−−−−−−−→ ≠ f 1 + · · · + f n

←−−−−−−−−−−−→

4

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