A Ton of Crap (73 page)

TRIGONOMETRY

Reciprocal Identities
Identities are true no matter what value the variable is. For example, the problem (
x
 + 3) (
x
 – 3) = 
x
²
 – 9 is always true. That makes it an identity. In trigonometry, there are several reciprocal identities one has to know.

The reciprocal identities are:

ALBERT EINSTEIN

Brownian Motion
In 1905, Einstein’s third paper concentrated on the random movement of small particles in liquids and gases. Brownian motion gets its name from Robert Brown, who in 1827, reported on the motion of pollen particles in water. Brown, however, was never able to figure out why the motion happened. Einstein figured out that the motion was due to water molecules hitting the pollen. Though the pollen grains were visible, the water molecules weren’t, and so it appeared that these particles were jiggling. Einstein was also able to show the speed the water molecules were moving in and how many molecules hit a single grain of pollen, as well as what properties of atoms could be tested.

CANTONESE

Cantonese Today
A total of 71 million people speak Cantonese, and it is spoken in Hong Kong, Guangdong, Macau, Hainan, and Guangxi. Through Western colonialism, migration, and trade, the majority of Chinese who have traveled abroad have been speakers of Cantonese. Today, Cantonese-speaking communities appear more in other countries than in most of China. The United States and Canada have the most
Cantonese-speaking communities outside of Hong Kong and mainland China, and in San Francisco, there are a total of 180,000 Cantonese speakers.

THE RUSSIAN REVOLUTION

The Aftermath
Lenin’s peace policy with Germany was widely unpopular and ended in Russia ceding large territories to the Germans. Following the October Revolution, a civil war broke out between the Whites (the anti-Bolsheviks) and the Reds (the Communists). The Reds eventually won after four years, and in 1922, the Soviet Union was established. When Lenin died in 1923, Joseph Stalin came to power.

HUMOR

David Sedaris
David Sedaris (whose sister is comedian Amy Sedaris) is one of the most prolific humorists writing today. His books usually consist of short essays full of biting, absurdist, and slightly neurotic commentary, based on his life. One of his most famous pieces, “Santaland Diaries,” was a memoir of his seasonal job working as an elf for Macy’s during the holiday season. He has published many books of his essays, one of his most well known being
Me Talk Pretty One Day
.

TRIGONOMETRY

Inverse Trigonometric Functions
When given the value of a function and asked to find the value of the angle, this is referred to as an inverse trigonometric function. The terms used for inverse functions are
arcsin
,
arccos
,
arctan
,
arccsc
,
arcsec
, and
arccot
. If
f
(
x
) = sin x and
g
(
x
) = arcsin 
x
, then the formula for finding the inverse trigonometric functions is
f
(
g
(
x
)) = 
x
or
g
(
f
(
x
)) = 
x
. So arcsin
x
 = 
y
, which leads us to the formula
x
 = sin 
y
.

ALBERT EINSTEIN

His Brain
Albert Einstein died on April 18, 1955, at the age of seventy-six. His body was cremated, but his brain was saved for research. Until 1999, it was decided that Einstein’s brain was really no different than any other person’s brain. In 1999 however, it was discovered that Einstein’s brain lacked a certain wrinkle, called the parietal operculum. To compensate for this lacking wrinkle, other parts of his brain, such as the inferior parietal lobes, had to compensate. This part of the brain plays a role in mathematical thinking and visual imagery.

CANTONESE

Useful Cantonese Phrases
Here are some helpful phrases to use when traveling to Hong Kong. Note that these are written in Yale Romanization, a phonetic English alphabet:

Hello.
Néih hóu.

Pleased to meet you.
Hóu hòisàm yihngsīk néih.

Good morning.
Jóusàhn.

Good day.
Ńgh ōn.

Good evening.
Máahn ōn.

Excuse me.
m̀hgòi.

How much is this?
Nīgo géidō chín a?

Thank you.
Dòjeh.

Where’s the toilet?
Chisó hái bīndouh a?

Do you speak English?
Neih sīkm̀hsīk góng yìngmán a?

Can you translate it for me?
Néih hóm̀hhóyíh bòng ngóh fáanyihk a?

Goodbye.
Joigin.

1. Lenin’s successful coup d’état, in which he and the Bolshevicks overthrew the Provisional Government, describes which of the following events?
   

   1. The February Revolution
      
   2. The October Revolution
      
   3. The events of International Women’s Day Festival
      
   4. The Summer of 1917
      

2. Which of the following happened after Lenin came to power?
   

   1. A peace policy with Germany that was widely unpopular
      
   2. Russia ceding large territories to the Germans
      
   3. A civil war between the Whites and the Reds
      
   4. All of the above
      

3. Which of the following was written by Mark Twain?
   

   1. Adventures of Huckleberry Finn
      
   2. A Confederacy of Dunces
      
   3. Me Talk Pretty One Day
      
   4. A and C
      

4. The Hitchhiker’s Guide to the
   Galaxy
   was written by:
   

   1. P. G. Wodehouse
      
   2. Terry Pratchett
      
   3. Douglas Adams
      
   4. David Sedaris
      

5. What is 60° in radians?
   

   1. π/3
      
   2. π/4
      
   3. π/2
      
   4. π
      

6. There is an oblique triangle ABC with side
   a
    = 9 inches, side
   b
    = 11 inches, and the angle of
   C
   is 60°. What is the value of
   c
   ?
   

   1. 103
      
   2. 10609
      
   3. Ö103
      
   4. Ö10609
      

7. What can we derive from
   Einstein’s special theory of
   relativity (
   E
    = 
   mc
   ²
   )?
   

   1. Mass is not energy.
      
   2. Mass is another form of energy.
      
   3. Light is another form of energy.
      
   4. The speed of light is not as fast as we thought.
      

8. Einstein’s theory of relativity can be broken up into what two parts?
   

   1. Special theory of relativity and Brownian motion
      
   2. General theory of relativity and Brownian motion
      
   3. Special theory of relativity and parietal operculum
      
   4. Special theory of relativity and the general theory of relativity
      

9. Which of the following is true?
   

   1. Though Cantonese is written in the standard language, it also has additional characters.
      
   2. There are words in Cantonese that do not have any meaning in Mandarin.
      
   3. Cantonese-speaking communities appear more in other countries than in China.
      
   4. All of the above.
      

10. Which of the following is true?
    

    1. Cantonese has four tones and Mandarin has up to nine.
       
    2. Cantonese has up to nine tones and Mandarin only has four.
       
    3. Cantonese and Mandarin have the same number of tones.
       
    4. Cantonese has four tones and Mandarin has five.