A combination of African & Irish traditional dancing may be the source of this style of dance
tap dance
I'm going to grab some this, meaning sleep
In one version his daughter is among the items he turns to gold with his touch
King Midas
That joker in home room who makes everybody laugh all the time
class clown
Ox
oxen
Drums called pahu help provide the rhythm for this sensuous dance of the Pacific
Hula
The opposing team doesn't score while losing
a shut-out
My theorem? That you know this whiz who gave his name to the equation a2 + b2 = c2
Pythagoras
Laid back dude who's always hanging out at or near the seashore
a beach bum
Cactus
cacti
These insects do a "dance" to communicate the location of distant flowers & nectar
bees
A courtesy one may take you from the airport to a rental car
shuttle
We're 100/100ths sure that Simon Stevin introduced the concept of "decimal" these to Europe in 1585
fractions
A friend in a distant land to whom you write letters
pen pal
Moose
Moose
Edgar Degas, who painted the dancer seen here, was part of this artistic movement

Impressionism
One who rarely leaves home, confined by introversion or illness
a shut-in
The ancient Greek Hipparchus pioneered this branch of math, from ancient Greek for "triangle" & "measure"
trigonometry
A very large person who seems quite passive & mild
a gentle giant
Forum
fora
The samba is a dance of this largest South American nation
Brazil
The device that opens and closes to expose the film in a camera.
shutter
In mythology Prometheus isn't chained to that rock forever; this hero rescues him
Hercules
Adjective for a mission just for scoping things out & gathering information
hint: F
fact-finding
Millennium
Millennia