Title: Geometry Applications: Translations in 3 Dimensions

Title: Geometry Applications: Translations in 3 Dimensions

[Music]

[Music]

THE PORT OF LOS ANGELES IS ONE OF THE BUSIEST

IN THE COUNTRY.

EVERY YEAR CARGO SHIPS LOADED WITH PRODUCTS

FROM AROUND THE WORLD ARRIVE AT THIS PORT,

AND JUST AS MANY SHIPS LOADED WITH

AMERICAN PRODUCTS LEAVE FROM THIS PORT.

THE MULTI-COLORED BOXES THAT YOU SEE ON THE SHIP

AND ON THE DOCKS ARE CARGO CONTAINERS.

EACH CONTAINER IS FILLED WITH

THE PRODUCTS BEING TRANSPORTED.

ONCE A CONTAINER HAS ARRIVED AT THE PORT,

THEN IT IS TRANSPORTED TO ITS FINAL DESTINATION

BY MEANS OF A TRUCK OR TRAIN.

MANY OF THE PRODUCTS THAT YOU USE AND EVEN

SOME OF THE FOOD YOU EAT MADE ITS WAY TO YOUR HOME

BY WAY OF A CARGO SHIP.

THIS PRACTICE OF USING CARGO CONTAINERS FOR

DELIVERING PRODUCTS IS CALLED CONTAINERIZATION,

AND CONTAINERIZATION HAS CONTRIBUTED GREATLY

TO THE GROWTH OF THE GLOBAL ECONOMY.

A FULLY LOADED CARGO SHIP CAN HAVE HUNDREDS

OF CONTAINERS STACKED ATOP ONE ANOTHER.

WHAT MAY LOOK LIKE A RANDOM ORGANIZATION OF CONTAINERS

IS ACTUALLY A WELL ORGANIZED ARRANGEMENT OF DATA.

FOR EXAMPLE, SUPPOSE THIS CARGO SHIP IS LOADED WITH

CONTAINERS HEADED FOR HAWAII AND AUSTRALIA.

IT WILL UNLOAD SOME CARGO IN HAWAII

AND THE REST IN AUSTRALIA.

SO IT MAKES SENSE TO HAVE THE CONTAINERS

BOUND FOR AUSTRALIA AT THE BOTTOM OF THE STACK

AND THOSE FOR HAWAII AT THE TOP OF THE STACK.

THIS WAY WHEN THE CARGO SHIP MAKES ITS FIRST STOP

IN HAWAII THE CONTAINERS THAT NEED TO BE UNLOADED

ARE WITHIN EASY REACH AND CAN BE UNLOADED QUICKLY.

NOW AMONG THE CONTAINERS HEADED TO EACH DESTINATION,

SOME CONTAINERS ARE HEAVIER THAN OTHERS.

THE CONTAINERS ARE SUCH THAT YOU CAN STACK THEM

ATOP ONE ANOTHER

REGARDLESS OF THE WEIGHT OF THE CONTAINER.

BUT TO MAKE IT EASIER TO LOAD AND UNLOAD CONTAINERS,

THE HEAVIER CONTAINERS SHOULD BE AT THE BOTTOM

AND THE LIGHTER ONES AT THE TOP.

THERE ARE MANY OTHER CRITERIA THAT GO INTO

DETERMINING THE MOST EFFICIENT WAY

OF LOADING A CARGO SHIP.

THE BASIC NOTION IS THAT THE LAST ITEMS LOADED

ARE THE FIRST TO BE UNLOADED.

THE ACRONYM, LIFO, FOR "LAST IN FIRST OUT"

IS A TYPE OF DATABASE ARRANGEMENT

THAT LEADS TO THE MOST EFFICIENT MEANS

OF LOADING AND UNLOADING A CARGO SHIP.

SUPPOSE YOU WANTED TO CREATE AN AUTOMATED SYSTEM

FOR LOADING CARGO ON A SHIP;

A COMPUTER PROGRAM THAT MANAGES THE CRANES

USED TO LOAD THE CONTAINERS.

YOU HAVE THE DATA ON THE DESTINATION

AND WEIGHT OF EACH CONTAINER.

SO THE PROGRAM WOULD NEED TO SORT THE DATA

INTO A LIFO LIST FOR LOADING THE SHIP.

BUT HOW DOES THE PROGRAM KNOW WHERE TO PLACE

EACH CONTAINER ON THE SHIP?

THIS IS WHERE WE GET TO THE GEOMETRIC CONSIDERATIONS.

AS YOU CAN SEE, EACH CONTAINER IS A

RECTANGULAR PRISM OF A STANDARD SIZE.

THINK OF EACH CONTAINER AS A BUILDING BLOCK

USED TO CREATE A LARGER RECTANGULAR PRISM.

WE CAN USE A THREE-DIMENSIONAL

RECTANGULAR COORDINATE SYSTEM TO MAP THE

COORDINATES OF EACH CONTAINER.

IN A THREE-DIMENSIONAL SYSTEM EACH POSITION

HAS THREE COORDINATES RELATIVE TO X, Y, AND Z.

NOW EACH RECTANGULAR PRISM IS MORE THAN

JUST A SINGLE POINT IN SPACE.

BUT FOR SIMPLICITY WE WILL BE TRACKING

THE COORDINATES THAT CORRESPOND TO

ONE OF THE CORNERS OF THE CONTAINER AS SHOWN HERE.

FURTHERMORE, EVEN THOUGH THE RECTANGULAR PRISM

HAS DIFFERENT LENGTH AND WIDTH DIMENSIONS,

WE WILL ADJUST THE COORDINATE GRID

SO THAT EACH SIDE OF THE CONTAINER

IS ONE UNIT LONG, AS SHOWN HERE.

THIS CONTAINER WITH THIS ORIENTATION

HAS COORDINATES (0,0,0)

WHICH IS THE CORNER POINT HIGHLIGHTED.

SO THE CONTAINERS ARE ARRANGED ON THIS

COORDINATE GRID AS THEY WOULD BE ON A CARGO SHIP.

BY ASSIGNING DISCRETE THREE DIMENSIONAL

COORDINATES TO EACH CONTAINER,

THE AUTOMATED SYSTEM KNOWS WHERE TO PLACE A CONTAINER.

SUPPOSE THAT A SHIP CAN HOLD 27 CONTAINERS

ARRANGED AS A 3X3X3 STACKED SET.

THIS GENERATES 27 xp COORDINATES.

THIS TABLE SUMMARIZES THE 27 COORDINATES

AND THEY ARE ARRANGED IN THE LIFO FORMAT.

IN OTHER WORDS, THE FIRST COORDINATE

IS THE FIRST CONTAINER TO BE LOADED,

AND THE LAST COORDINATE IS THE

LAST CONTAINER TO BE LOADED,

WHICH IS ALSO THE FIRST CONTAINER TO BE UNLOADED.

AS FOR THE CARGO ITSELF, THIS TABLE SHOWS THE

DESTINATION AND WEIGHT OF EACH CONTAINER.

THERE ARE TWO DESTINATIONS,

HAWAII AND AUSTRALIA, DESIGNATED BY "H" AND "A".

SINCE THE CONTAINERS ARRIVED AT THE DOCK FROM

DIFFERENT LOCATIONS, THEY ARE ARRANGED

IN RANDOM ORDER AND NOT IN THE LIFO FORMAT.

AS A LOGISTICS MANAGER FOR A SHIPPING COMPANY,

YOUR JOB IS TO ARRANGE THE CONTAINERS

IN THE MOST EFFICIENT ORDER POSSIBLE

AND MAP THEM TO THE 27 xp COORDINATES.

THE AUTOMATED CARGO CRANES WILL THEN ASSEMBLE

THE CONTAINERS USING THE COORDINATES AS THE ENDPOINTS

OF A THREE DIMENSIONAL TRANSLATION.

LET'S USE THE TI-NSPIRE TO SOLVE THIS PROBLEM.

TURN ON THE TI-NSPIRE.

CREATE A NEW DOCUMENT.

YOU MAY NEED TO SAVE A PREVIOUS DOCUMENT.

CREATE A LIST AND SPREADSHEET WINDOW.

PRESS THE UP ARROW TO MOVE TO THE VERY TOP OF COLUMN A.

INPUT THE HEADING "DESTINATION"

AND PRESS TAB TO GO TO THE NEXT COLUMN.

INPUT THE HEADING "WEIGHT" AND PRESS ENTER.

USE THE NAVIGATION ARROWS TO MOVE TO CELL A1.

INPUT THE FOLLOWING DATA AS SHOWN IN THIS TABLE.

PAUSE THE VIDEO TO INPUT THE DATA.

THE DATA THAT YOU INPUT IS NOT IN THE CORRECT ORDER

FOR LOADING THE CARGO SHIP, BUT SIMPLY REFLECTS

HOW THE CONTAINERS ARE ARRANGED ON THE DOCK.

WE WANT TO ORGANIZE THE DATA BY DESTINATION AND WEIGHT.

DESTINATION IS THE PRIMARY WAY OF SORTING THE DATA,

SO WE WANT TO SORT THE ENTIRE DATA SET.

MOVE THE CURSOR TO THE VERY TOP OF COLUMN A

WHERE THE COLUMN HEADING IS.

THEN PRESS THE UP ARROW ONE MORE TIME TO SELECT

THE ENTIRE COLUMN, WHICH SHOULD BE HIGHLIGHTED.

PRESS THE SHIFT KEY AND THE RIGHT ARROW

TO HIGHLIGHT ALL OF COLUMN B.

WITH ALL OF THE DATA HIGHLIGHTED, SORT IT.

PRESS MENU AND UNDER ACTIONS SELECT SORT.

THE PRIMARY CONSIDERATION IN ARRANGING THE DATA

IS THE DESTINATION.

CONTAINERS GOING TO AUSTRALIA GET LOADED FIRST.

BY DEFAULT, THE SPREADSHEET SORTS THE DATA

IN ASCENDING ORDER WHICH COINCIDES WITH WHAT WE WANT.

THIS IS ONLY BECAUSE THE "A" IN AUSTRALIA

COMES BEFORE THE "H" IN HAWAII.

OTHERWISE YOU WOULD SORT THE DATA IN DESCENDING ORDER

- FOR EXAMPLE, IF THE FINAL DESTINATION WAS CHINA.

TAB YOUR WAY TO "OK" AND PRESS ENTER.

YOUR DATA IS NOW ORGANIZED BY DESTINATION.

SCROLL DOWN THE SPREADSHEET TO VERIFY.

AS YOU DO, YOU'LL NOTICE THAT

WITHIN EACH DESTINATION GROUP THE CONTAINERS

ARE STILL NOT ARRANGED FROM HEAVIEST TO LIGHTEST.

RECALL WE WANT THE HEAVIER CONTAINERS AT THE BOTTOM,

SO THOSE NEED TO BE LOADED FIRST.

AS A RESULT, THE DATA NEEDS WHAT'S CALLED

A SECONDARY SORT.

THE PRIMARY SORT WAS TO ARRANGE THE DATA

BY DESTINATION.

THE SECONDARY SORT IS TO ARRANGE THE DATA

WITHIN THE PRIMARY SORT BY WEIGHT,

BUT THIS TIME IN DESCENDING ORDER.

SO MOVE THE CURSOR TO CELL A1.

HOLD THE SHIFT KEY WHILE PRESSING THE DOWN

AND RIGHT ARROWS TO SELECT ALL THE CELLS

THAT HAVE THE DATA FOR AUSTRALIA.

YOUR SCREEN SHOULD LOOK LIKE THIS.

IF YOU NEED TO START OVER, PRESS ESCAPE,

GO BACK TO CELL A1 AND START HIGHLIGHTING.

WITH THE DATA HIGHLIGHTED

YOU ARE NOW READY FOR THE SECONDARY SORT.

PRESS MENU AND UNDER ACTIONS SELECT SORT.

AS NOTED EARLIER, THE DEFAULT SETTINGS

ARE TO SORT ALONG COLUMN A IN ASCENDING ORDER.

IN THIS CASE YOU WANT TO SORT THE DATA IN COLUMN B

IN DESCENDING ORDER, SO PRESS THE DOWN ARROW

TO SELECT COLUMN B FROM THE DROP DOWN MENU.

PRESS ENTER.

PRESS TAB TO GO TO THE NEXT DROP DOWN MENU.

USE THE DOWN ARROW TO SELECT DESCENDING.

PRESS ENTER.

PRESS TAB TO HIGHLIGHT THE "OK" BUTTON AND PRESS ENTER.

YOUR DATA FOR AUSTRALIA IS NOW ARRANGED

IN DESCENDING ORDER.

REPEAT THIS PROCESS FOR THE HAWAII DATA.

MOVE THE CURSOR TO THE FIRST CELL IN COLUMN A

THAT HAS THE HAWAII DATA.

HOLD THE SHIFT KEY AND PRESS THE DOWN AND RIGHT

ARROW KEYS TO HIGHLIGHT ALL OF THE DATA FOR HAWAII.

WITH THE DATA HIGHLIGHTED, PRESS MENU

AND UNDER ACTIONS SELECT SORT.

PRESS THE DOWN ARROW TO SELECT COLUMN B

FROM THE DROP DOWN MENU.

PRESS ENTER.

PRESS TAB TO GO TO THE NEXT DROP DOWN MENU.

USE THE DOWN ARROW TO SELECT DESCENDING.

PRESS ENTER.

PRESS TAB TO HIGHLIGHT "OK" AND PRESS ENTER.

NOW ALL 27 DATA ITEMS ARE ARRANGED

ACCORDING TO DESTINATION AND WEIGHT.

THIS ARRANGEMENT CAN BE MAPPED TO THE

APPROPRIATE COORDINATES THAT DETERMINE

WHERE ON THE SHIP EACH CONTAINER WILL BE LOCATED.

THESE 27 CONTAINERS ARE STACKED ON THE

LOADING DOCKS AND SO EACH CONTAINER HAS ITS OWN

INITIAL COORDINATES WHERE IT IS LOCATED.

TAKING THESE COORDINATES AND THE COORDINATES FOR

WHERE THE CONTAINER SHOULD BE LOCATED ON THE SHIP,

AN AUTOMATED SYSTEM FOR LOADING THE CONTAINERS

CAN TAKE BOTH SETS OF COORDINATES

AND USE THEM TO LOAD THE SHIP.

OF COURSE, AUTOMATED DOESN'T MEAN

THAT PEOPLE AREN'T INVOLVED.

DOCK WORKERS ARE STILL A KEY PART OF

MAKING SUCH A SYSTEM WORK.

BUT AUTOMATING THE WORK OF LOADING AND UNLOADING

CONTAINERS CREATES AN EFFICIENT SYSTEM

FOR DEALING WITH THE HUGE NUMBER OF CONTAINERS

THAT ARRIVE AT PORTS AROUND THE WORLD.

THE MOVEMENT OF CONTAINERS TO AND FROM A SHIP

IS AN EXAMPLE OF A GEOMETRIC TRANSLATION

IN A THREE DIMENSIONAL COORDINATE SYSTEM.

SUCH AUTOMATED SYSTEMS CAN BE USED

IN MANY DIFFERENT WAYS.

EVEN WITHIN THE CASE OF CONTAINER SHIPS,

IT IS POSSIBLE TO HAVE MULTIPLE DESTINATIONS

FOR CARGO.

FOR EXAMPLE, A CONTAINER SHIP LEAVING THE PORT OF L.A.

MIGHT STOP AT HAWAII, AUSTRALIA, NEW ZEALAND,

JAPAN, AND FINALLY CHINA.

AT EACH PORT CONTAINERS WOULD BE UNLOADED,

BUT ALSO NEW ONES WOULD BE LOADED,

ADDING AN ADDITIONAL COMPLICATION

TO THE SORTING AND ARRANGING OF CONTAINERS.

IN THE REAL WORLD OF IMPORTING AND

EXPORTING CARGO THE DATA MANAGEMENT NEEDS

ARE VERY COMPLEX, SO AUTOMATED SYSTEMS

ARE A NECESSITY FOR TODAY'S GLOBAL ECONOMY.