# Geometry and Halloween Costumes

From a friend’s Facebook post (shared with her permission):

For every time a geometry student asks, “When am I ever going to use this in real life?” Well, if your child ever asks you to make her a Harley Quinn costume, and there is no pattern, so you have to draft your own, you will need to find the sides of a square using the measurement of the diagonal…

[I]f you need to have a square patchwork of different colored fabrics which line up on diagonal points for a specific measurement so that you have four colored diagonal squares from the shoulder to just below the waist, you would need to find the measurement of the four equal sides of each square. Then you would add seam allowances so you could cut the squares out of the different colored fabrics and sew them together in exact lines to line up just right so you could make a top that looks like the top the character wears. And since this character is only a cartoon character who has been made into a little doll, not many people out there in the world have yet attempted an actual costume to be worn by a real live girl. Of course, a person could just take a pencil and a ruler and draw squares, but without using math, that person could not put together a patchwork of colored fabric squares with this result.

The finished product:

# My Mathematical Magic Show: Part 9

This mathematical trick was not part of my Pi Day magic show but probably should have been. I first read about this trick in one of Martin Gardner‘s books when I was a teenager, and it’s amazing how impressive this appears when performed. I particularly enjoy stumping my students with this trick, inviting them to figure out how on earth I pull it off.

Here’s a video of the trick, courtesy of Numberphile:

Summarizing, there’s a way of quickly determining $x$ given the value of $x^5$ if $x$ is a positive integer less than 100:

• The ones digit of $x$ will be the ones digit of $x^5$.
• The tens digit of $x$ can be obtained by listening to how big $x^5$ is. This requires a bit of memorization (and I agree with the above video that the hardest ones to quickly determine in a magic show are the ones less than $40^5$ and the ones that are slightly larger than a billion):
• 10: At least 10,000.
• 20: At least 3 million.
• 30: At least 24 million.
• 40: At least 100 million.
• 50: At least 300 million.
• 60: At least 750 million.
• 70: At least 1.6 billion.
• 80: At least 3.2 billion.
• 90: At least 5.9 billion.

# Random couscous snaps into beautiful patterns

I enjoyed watching this.

# A request to the athletic department

Even though I’ve had nothing but good professional relationships with the athletic department at my own university, I still think this is really funny.

Source: http://imgur.com/vJWkqhe

Here’s a standard joke involving representing numbers in different bases.

A: 57,005.

The joke, of course, is that $DEAD$ can be considered a number written in base 16, using the usual convention $A = 10$, $B = 11$, $C = 12$, $D = 13$, $E = 14$, and $F = 15$. In other words, $DEAD$ can be converted to decimal as follows:

$DEAD_{\small sixteen} = 13 \times 16^3 + 14 \times 16^2 + 10 \times 16 + 13 = 57,005$.

After I heard this joke, I wondered just how many English words can be formed using only the letters A, B, C, D, E, and F so that I could make a subtle joke on a test. To increase the length of my list, I also allowed words that included the letters O (close enough to a 0), I (close enough to 1), and/or S (close enough to 5). However, I eliminated words that start with O (since a numeral normally doesn’t start with 0) and/or end in S (the plural version of these words are easily formed).

So I wrote a small program to search the dictionary that I have on my computer. The unabridged list follows, with words beginning with a capital letter (such as names or places) listed at the bottom. I emphasize that this list is unabridged, as there are several words on this list that I wouldn’t place on a test for obvious reasons: I would never ask my class to convert the base-10 numeral 721,077 into hexadecimal just so they can obtain the answer of $B00B5$.

a

abaci

abase

abased

abbé

abed

abide

abided

abode

aboded

abscessed

abscissa

abscissae

acacia

accede

acceded

accessed

ace

aced

acid

acidic

acidified

aid

aide

aided

aside

assessed

b

baa

baaed

babe

babied

baobab

base

based

basic

bassi

basso

be

bed

bedded

bedside

bee

beef

beefed

beside

biased

biassed

bib

bid

bide

bided

boa

bob

bobbed

bode

boded

bodice

boo

boob

boobed

booed

bossed

c

cab

cabbed

cabbie

caboose

cacao

café

case

cased

cassia

cease

ceased

cede

ceded

cob

cobbed

cocci

cocoa

cod

coda

codded

code

coded

codified

coed

coffee

coif

coifed

coiffed

coo

cooed

d

dB

dab

dabbed

deaf

deb

debase

debased

decaf

decease

deceased

decide

decided

decode

decoded

deed

deeded

deface

defaced

defied

deice

deiced

deified

dice

diced

did

die

died

diocese

diode

disc

disco

discoed

disease

diseased

dissed

do

doc

dodo

doe

doff

doffed

dose

dosed

e

ease

eased

ebb

ebbed

eddied

edifice

edified

efface

effaced

f

fa

face

faced

fed

fee

feed

fiasco

fib

fibbed

fie

fief

fife

fob

fobbed

foci

foe

food

i

ice

iced

id

idea

if

sac

safe

said

sassed

scab

scabbed

scoff

scoffed

sea

seabed

seafood

seaside

secede

seceded

see

seed

seeded

sic

side

sided

so

sob

sobbed

sod

soda

sodded

sofa

A

Abbasid

Abe

Ac

Aida

Asia

Assisi

B

Ba

Basie

Be

Bede

Beebe

Bessie

Bi

Bib

Bic

Bob

Bobbi

Bobbie

Boccaccio

Boise

Bose

C

Ca

Case

Casio

Cassie

Cd

Cf

Ci

Cid

Co

Cobb

D

Dacca

Debbie

Dec

Decca

Dee

Defoe

Di

Dido

Doe

E

Eco

Ed

Edda

Eddie

Effie

Essie

F

Fe

Feb

Fed

Fido

I

Iaccoca

Ibo

Ida

Io

Isaac

Issac

# Combinatorics and Jason’s Deli: Index

I’m doing something that I should have done a long time ago: collecting a series of posts into one single post. The following links comprised my series on an advertisement that I saw in Jason’s Deli.

Part 2: Correct calculation of the number of salad bar combinations.

Part 3: Incorrect calculation of how long it would take to eat this many combinations.

# Logic puzzle

Jack is looking at Anne, Anne is looking at George. Jack is married, George is not. Is a married person looking at an unmarried person?

I’ll refer the interested reader to the above link for the answer; I’m happy to report that I got this one right.

# Defining Gravity

I’m in nerd heaven: Sir Isaac Newton and Albert Einstein parodying a showstopper from Wicked.