>> OH, HEY.
YOU MUST BE THE BLACK WIDOW.
>> THAT'S RIGHT.
AND YOU ARE?
>> OH, PEOPLE LIKE TO CALL ME.
008.
[CRACKLING, THEN LOW HUMMING]
[CRACKLING; LOW HUMMING STOPS]
>> I THINK YOU NEED
NEW BATTERIES.
>> STUPID.
[CAPTIONING MADE POSSIBLE BY
ESPN, INC.]
>> SPORTS FIGURES 
PUT YOUR BRAIN IN THE GAME.
>> YOU KNOW, THE THING THAT
SEPARATES THE REAL GREAT
POOL PLAYERS FROM THE REST OF US
IS THE FABULOUS BANK SHOTS
THAT THEY MAKE.
ONE WAY TO UNDERSTAND BANK SHOTS
IS JUST LOOK IN THE MIRROR.
HEY, GUYS, YOU WANT TO GET
THE 12 BALL IN THE CORNER POCKET
OVER THERE
>> YOU'RE NOT ALLOWED TO
PLAY OFF THE 8 BALL,
SO YOU'RE GONNA HAVE TO
BANK IT OFF THIS RAIL.
>> OK, CHECK THIS OUT.
IF I AIM FOR THE REFLECTION
OF THE 12 BALL IN THE MIRROR,
I SHOULD BE ABLE TO HIT IT.
I THINK WE NEED TO
WATCH THAT AGAIN.
I HIT THE CUE BALL AT
THE REFLECTION OF THE 12 BALL
IN THE MIRROR.
WATCH THE CUE BA.
IT LOOKS LIKE IT GOES
STRAIGHT THROUGH THE MIRROR
TO THE 12.
WHAT WE'VE BEEN LOOKING AT
IS THE PRIIPLE OF REFLECTION.
GEOMETRY TELLS US THAT
THE ANGLE  INCIDENCE EQUALS
THE ANGLE OF REFLECTION.
OH!
LET'S POSITION MARY AND TAMARA
SO THEY CAN SEE EACH OTHER'S
EYES IN THE MIRROR.
WE'LL MARK THAT INT AND EXTEND
THE LINE FROM EACH OF THEIR EYES
TO WHERE THEY SEE EACH OTHER.
WHEN LOOKING AT REFLECTION
PROBLEMS, WE DRAW WHAT'S CALLED
THE NORMAL LE.
IT FORMS A RIGHT ANGLE
TO THE LINE OF REFLECTION;
IN THIS CASE, THE MIOR.
OK, NOW LET'S LABEL
ALL OUR POINTS.
THE POINT AT THE MIRROR
WE'LL CALL "O."
FROM THE TOP OF THE NORMALINE,
"N."
MARY'S EYES ARE POINT "M,"
AND TAMARA'S EYES ARE POINT "T."
CHECK IT OUT:
EVEN THOUGH NES "MO" AND "TO"
ARE DIFFERENT LENGTHS,
THE ANGLES "MON" AND "TON"
ARE EQUAL.
SO WHAT DOES SHE KNOW
THAT WE DON'T?
THAT'S JEANETTE LEE,
ALSO KNOWN AS THE BLACK WIDOW.
SHE WAS A GOLD MEDALIST
 THE 2001 WORLD GAMES.
SHE'S ALSO BEEN RANKED IN
THE TOP 3 PLAYERS IN THE WORLD
FOR THE PAST 10 YEARS.
AND SHE'S A MEMBER OF
E WOMEN'S SPORTS ASSOCIATION
AND THE SCOLIOSIS FOUNDATION.
BUT SHE'S GOING TO HELP US
WITH OUR KICK SHOT.
NICE SHOT.
SO TELL ME, JEANETTE, DO YOU
USE THE ANGLE OF INCIDCE
AND THE ANGLE OF REFLECTION
ALL THE TIME IN BILLIARDS?
>> ABSUTELY.
WE WORK WITH IT EVERY DAY.
IT'S ESSENTIAL IN
EVERY SINGLE KICK SHOT.
 WELL, LOOK, I DON'T WANT YOU
GIVING AWAY ANY TRADE SECRETS,
BUT CAN YOU EXPLAIN IT TO US?
>> SURE. IT'S NOT A SECRET.
IT'S JUST SIMPLE SCIENCE.
IF I HIT A BALL WARDS
THE CUSHION, THE PATH
IT TRAVELS GIVES US A LINE.
THBALL BOUNCES OFF
THE CUSHION, AND ITS NEW PATH
GIVES US A SECOND LINE.
NOW, IF WE WERE TO MEASURE
THE ANGLES FORMED BY THE PATH
OF THE BALL, WE WOULD ND
THAT THEY ARE EXACTLY THE SAME
ON EITHER SIDE OF
WHERE THE BALL BOUNCED.
WE CALL THE ANGLE CREATED
BY THE BALL'S APPROACH
THE ANGLE OF INCIDENCE.
WE CALL THE ANGLE CREATED
BY THE BALL'S BOUNCE
AND THE NEW PATH
THE ANGLE OFEFLECTION.
ALL IT MEANS IS, AN OBJECT IS
GONNA BOUNCE O OF SOMETHING
AT THE SAME ANGLE THAT IT HIT,
SO THE TWO PATHS
ARE SYMMETRICAL.
>> DON'T YOU LOVE GEOMETRY?
WHEN WE HAVE A SHAPE
THAT CAN BE CUT IN HALF,
AND BOTH SIDES ARE THE SAME,
IT'S CALLED SYMMET--
OR WE SAY THE OBJECTS
ARE SYMMETRICAL.
REFLECTIONS, LIKE IN A MIRROR
OR OFF OF A BILLIARD TABLE,
ARE WAYS SYMMETRICAL.
WE CALL THAT KIND OF SYMMETRY
REFLECTIONAL SYMMETRY,
OR LINE SYMMETRY.
THAT MEANS THERE'S AINE
WHERE WEOULD FOLD THE OBJECT
IN HALF, AND BOTH SIDES
WOULD MATCH PERFECTLY.
OK, JEANETTE, BUT THERE ARE
SOME LIMITATIONS TO THIS
EQUAL ANGLE THING.
 RIGHT.
IT ONLY WORKS OFF THE CUSHION.
IF IT COMES OFF AN OBJECT BALL,
IT'S A WHO 'NOTHER THING.
>> BUT WITH THE CUSHION?
>> WITH THE CUSHION, IF YOU WANT
TO COME OFF AT AN EQUAL ANGLE,
YOU HAVE TO MAKE SURE THAT YOU
HIT AT A REASONABLE SPEED
AND WITHOUT ANY ENGLISH
ONHE CUE BALL.
>> OH, "ENGLISH."
THAT'S POOL PLAYER FOR "SPIN,"
RIGHT?
>> RIGHT.
ENGLISH CHANGES THE WAY THE CUE
BALL COMES OFF THE CUSHION.
SO IN ORDER TO AVOID THAT,
YOU HAVE TO MAKE SURE YOU HIT
THE CUE BALL EXACTLY
IN THE CENTER.
>> BUT DON'TOU GUYS SOMETIMES
USE ENGLISH OFF THE CUSHIONS?
>> DEFINITELY.
>> OK, WELL, UM.
FOR MORE ON ENGLISH, LET'S GO
TO THE SPORTS FIGURES BLACKBOARD
AND COMMENTATOR MITCH LAURANCE.
>> WHEN YOU PUT SIDE SPIN ON
A CUE BALL, S CALLED ENGLISH,
AND ENGLISH IS ALL ABOUT
AFFECTING THE WAY A BALL
IS GOI TO REBOUND OFF A RAIL.
WE'VE ALREADY SEEN
THAT A BALL WITH NO SPIN
WILL FORM EQUAL ANGLES
OF APPROACH AND DEPARTURE.
GLE OF INCIDENCE EQUALS
ANGLE OF REFLECTION.
TO PUT ENGLISH ON THE CUE BALL,
E PLAYER HITS THE BALL
OFF CENTER, LEFT OR RIGHT.
FOR THE CUE BALL TO REFLECT
AT A LESSER ANGLE OFF THE RAIL,
YOU HIT THE CUE BALL
WITH RIGHT ENGLISH,
OR WHAT WE CALL REVERSE ENGLISH.
THAT'S SPIN IN THIS RECTION,
AND WATCH WHAT HAPPENS
OFF THE RAIL.
IF THE PLAYER WANTS THE BALL
TO REFLECT AT A GREATER ANGLE,
THEY'LL PUT LEFT ENGLISH
ON THE BALL, OR WHAT WE CALL
RUNNING ENGLISH.
ALL PROFESSIONALS USE ENGLISH
TO CHANGE THE WAY THE CUE BALL
REFLECTS OFF A RAIL.
FOR MOST PEOPLE, THOUGH,
IT'S HARD ENOUGH JUDGING
THE ANGLES WHEN YOU'RE KICKING
A BALL OFF A RAIL WITH NO SPIN.
SO REMEMBER,
START WITH THE BASICS.
TO HAVE THE CUE BALL REBOUND
WITH THE ECT SAME ANGLE
AS IT APPROACHES A RAIL,
YOU HAVE TO HIT THE CUE BALL
DEAD CENTER, NO SPIN.
I'M MITCH LAURANCE AT
THE SPORTS FIGURES BLACKBOARD.
>> TELL ME, BLACK WIDOW,
DO YOU HAVE A PERSONAL WORKOUT
ROUTINE THATOU HAVE TO DO
FOR THE SPORT?
>> ABSOLUTELY.
I ALWAYS MAKE SURE THAT
I STRETCH COMPLETELY,
PARTICULARLY MY TRICEPS
AND THINGS LE THAT, BECAUSE
WHEN YOU'RE GOING DOWN TO SHOOT,
YOU GET A FULL EXTENSION THERE,
AND ALSOELPS ON THE BREAKS.
SO I'M ALWAYS DOING KICKBACKS
AND TRICEP DIPS AND WORKING
THAT OUT THERE.
YOU HAVE TO DO BACK WORK--
YOU KNOW, STRENGTHEN MY BACK
ON DIFFERENT MACHINES, AND ALSO
CRUNCHES AND THINGS LIKE THAT--
KEEPING YOUR STOMACH REAL TIGHT.
BUT ETTY MUCH YOUR STOMACH,
YOUR BACK, MOSTLY UPPER BODY.
AND THE MOST IMPORTANT THING
IS ABOUT YOUR LEGS, IS NOT
REALLY GETNG REALLY STRONG AS
MUCH AS STAYING VERY FLEXIBLE.
AND THEN YOU WANT TO DO
CARDIO WORKOUTS TO BUILD YOUR
ENDURANCE, BECAUSE IF YOU HAVE
TO PLAY MATCH AFTER MATCH AFTER
MATCH, IT'REALLY HARD ON YOU.
>> PRETTY COOLRIGHT?
TO MAKE BANK SHOTS,
ALL YOU HAVE TO DO IS SHOOT
AT THE REFLECTION.
>>EAH, BUT YOU'RE NOT ALLOWED
TO USE MIRRORS.
>> TRUE. TRUE.
BUT WITH THE HELP OF SOME REALLY
SIMPLE GEOMETRY,E CAN LEARN
HOW TO DO IT WITHOUT MIRRORS.
BEUSE THE PRINCIPLE
OF REFLECTION WORKS THE SAME
FOR MIRRORS AS IT DOES
FOR BILLIARD BALLS,
OUR REFLECTIONN THE MIRROR
MAPS OUT THE REFLECTION
WE WANT THE BALL TO MAKE.
WHEN I HIT THE CUE BALL
TOWARD THE REFLECTED 12 BALL,
I CREATE TWONGLES:
ONE ON THE TABLE
WE'LL CALL ANGLE "AOB,"
AND ONE ON THE MIRROR
THAT WE'LL CALL ANGLE "A1OB1."
"O" IS THE POINT WHERE
THE BALL HITS THE CUSHION:
THE VERTEX OF OUR ANGLE.
THE CUSHION IS OUR
LINE OF REFLECTI.
LET'S CALL THAT LINE "RC."
NOW, IF WE CONNECT POINTS
"B" AND "B1",
OUR 12 BALL
AND REFLECTED 12 BALL,
WE HAVE CREATED A TRIANGLE, AND
LINE "RC" BISECTS THAT TRIANGLE
TO CREATE TWO SMALLER TRIANGLES.
LIKE WE SAW BEFORE,
WE WOULD ORDINARILY USE "N,"
THE NORMAL LINE,
FOR REFLECTION PROBLEMS,
BUT INSTEAD WE'LL USE LINE "RC."
EITHER ONE WILL WORK.
WE COULD MEASURE OUR ANGLES
TO PROVE THATHEY'RE EQUAL
ON EHER SIDE OF THE LINE
OF REFLECTION.
BUT THE BEAUTY OF THE PRINCIPLE
OF REFLECTION IS IT TELLS US
THE ANGLES ARE EQUAL,
SO WE DON'T VE TO.
WE CAN PROVE THAT OUR TWO
SMALLER TRIANGLES
ARE CONGRUENT--EQUAL.
GEOMETRY TELLS US THAT WHE
A LINE IERSECTS ANOTHER LINE,
THE VERTICAL ANGLES ARE EQUAL.
LINE "AB1" INTERSECTS LINE "RC,"
SO THE VERTICAL ANGLES "AOR"
AND "B1OC" MUST BE EQUAL.
WE KNOW ANGLE "AOR"
AND ANGLE "BOC"
ARE EQUAL BECAUSE OF
THE PRINCIPLE OF REFLECTION.
THEREFORE, ANGLE "BOC"
MUST EQUAL ANGLE "B1OC."
WE ALSO KNOW THAT EACH TRIANGLE
HAS A RIGHT ANGLE
HERE AND HERE.
LINE "OC" IS SHARED
BY BOTH TRIANGS.
WHEN YOU HAVE TWO EQUAL ANGLES,
AND THE SIDE BETWEENHE ANGLES
IS EQUAL, THE TRIANGLES
ARE CONGRUENT--EQUAL.
THAT MEANS THE REFLECTED BALL
IS AN EQUAL DISTANCE
OFF THE TABLE AS OUR REABALL
IS FROM THE LINE OF REFLECTION--
THE CUSHION.
OK, SO HOW CAN WE USE
THAT INFORMATION?
>> YOU C FIGURE OUT WHERE
THE REFLECTED 12 BALL WOULD BE.
THEN ALL YOU HAVE TO DO IS
AIM AT THE REFLECTED 12 BALL
TO HIT THE REAL 12 BALL.
>> HOW DO WE DO THAT?
 BY MEASURING.
JUST MEASURE THE DISTANCE
FROM THE 12 BALL TO THE CUSHION,
AND EXTEND THAT LINE OFF
THE TABLE THE SAME DISTANCE.
>> OK, LET'S DO IT.
>> OK, THANKS TO GEOMETRY,
WE KNOW THAT THAT IS WHERE
OUR REFLECTED 12 BALL WOULD BE.
OK, PATRICK, YOU WANT TO
TRY IT OUT?
YOU'RE NOT A PROFESSIONAL
BILLIARDS PLAYER, ARE YOU?
>> NO.
>> OK.
ALL PATRICK HAS TO DO IS AIM
FOR THE REFLECTED 12 BALL.
ALL RIGHT, DON'T CHOKE.
ESOME! HA HA HA!
ARE YOU SURE YOU'RE NOT
A PROFESSIONAL BILLIARDS PLAYER?
>> YEAH, I'M SURE.
>> SEE, THANKS TO INCIDENCE
AND REFLECTION, ANYBODY CAN MAKE
A FANCY BANK SHOT.
THAT WAS GOOD.
OOH, VERY IMPRESSIVE.
WE C FIGURE OUT HOW
THAT ONE WORKS, TOO.
>> OK.
>> FOR A TWO-CHION KICK SHOT,
WE JUST ADD ANOTHER MIRROR.
SO THIS MIRRORS REFLECTING
THAT MIRROR, SO IN THEORY,
I SHOULD BE ABLE TO
SHOOT AT THE RLECTION
 THE REFLECTION,
AND I SHOULD BE ABLE TO SINK IT.
>> THAT'S THE THEORY.
>> WELL, THERE'S ONLY ONE WAY
TO TEST IT.
>> OK.
WE HAD SOME ENGLISH.
COME ON. WHOO!
>> BUT, JEANETTE, YOU OW, I'M
USING MIRRORS TO MAKE THAT SHOT,
WHICH IS OBVIOUSLY CHEATING.
HOW DO YOU GUYS DO IT?
>> A LOT OF IT IS JUST PRACTICE.
WHAT YOU DO--WHAT I  IS,
I IMAGINE THAT THERE IS A MIRROR
ALONG THE RAIL, AND I PICTURE
IN MY MIND MENTALLY
WHERE THAT POCKET WOULD BE.
A LOT OFHAT IS, YOU KNOW,
YOU DO IT OVER AND OVER
AND OVER AGAIN AND AFTER AWHILE,
IT BECOMES NATURAL
THAT YOU CAN SEE IT.
>> RIGHT.
I GUESS YOU ALSO HAVE TO
WORK JUST ON THE MECHANICS
OF YOUR SWING, RIGHT?
>> RIGHT.
THAT'S THE DIFFICULT PART.
YOU CAN SEE ALL THE ANGLES
YOU WANT AND IMAGINE IT,
BUT IF YOU DON'T HIT EXACTLY
WHERE YOU WANT TO HIT
ON THE CUSHION AS WELL AS GET
THE SPEED RIGHT, IT'S--
IT WOULD BE VERY DIFFICULT.
>> AND THEN FINALLY, I MN,
ONCE YOU PUT THE TIME IN,
WOULDN'T YOU SAY
YOHAVE TO RELAX AND BELIEVE
THAT YOU CAN DO IT?
>> RIGHT. EXACTLY.
I THINK THAT YOU CAN PUT ALL
THE PRACTICE AND ALL THE TIME
INTO IT THAT YOU WANT, BUT ONC
IT COMESIME THAT YOU WANT
TO BEAT YOUR HUSBAND OR GO OUT
THERE AND KICK SOME BUTTS
AND YOU KNOW, STUFF LIKE THAT,
YOU'VE GOT TO THINK MORE ABOUT
HOW HUNGRY YOU ARE TO WIN
THAN HOW AFRAID YOU ARE TO LOSE.
AND THAT'S SO MUCH
ABOUT CONFIDENCE.
BUT IF YOU DON'T HAVE TH,
U MIGHT AS WELL THROW
ALL THAT WORK OUT THE WINDOW.
JUST BELIEVE IN YOURSELF.
>> OH...
THERE'S A PE OF GAME CALLED
3-CUSHION IN WHICH THE CUE BALL
HAS TO REFLECTFF 3
OF THE CUSHIONS BEFORE IT HITS
THE OBJECT BALL.
SO THE WHO GAME
IS ABOUT REFLECTION.
OH...
OK, GUYS, SO WHAT HAVE
WE LRNED?
>> THE LAW OF REFLECTION.
>> THAT SAYS THAT THE ANGLE
OF IIDENCE EQUALS THE ANGLE
OF REFLECTION.
THEY'RE SYMMETRICAL.
>> REFLECTIONAL SYMMETRY IS WHEN
YOU COULD FOLD SOMETHING IN HALF
AND BOTH SIDES MATCH UP
PERFECTLY.
>> AND WE PROVED THIS ALL TRUE
USING GEOMETRY.
>> WELL, THAT'S IT.
WE'D LIKE TO THANK JEANETTE LEE,
MITCH LAURANCE, AMSTERDAM
BILLIARDS, AND OUR STUDENTS
PATRICK, MICHAEL, DEANA,
AND JESSICA FOR HELPING US OUT
HERE TODAY O
ESPN SRTS FIGURES: 
REFLECTING ON BILLIARDS. 
SWEET. HA HA HA!
