Title: Geometry Applications: Geometry Basics

Title: Geometry Applications: Geometry Basics

[Music]

[Music]

THE ARECIBO OBSERVATORY IN PUERTO RICO

IS ONE OF THE LARGEST RADIO TELESCOPES ON EARTH

AND HAS BEEN USED TO MAKE SOME IMPORTANT DISCOVERIES

IN OUR SOLAR SYSTEM.

THE SOLAR SYSTEM IS MADE UP OF THE SUN,

THE PLANETS AND THEIR MOONS

AND OTHER CELESTIAL OBJECTS IN THE VICINITY OF THE SUN.

AS THE EARTH ROTATES AROUND THE SUN

ITS MOTION THROUGH SPACE IS ALONG A PLANE

THAT INTERSECTS THE SUN.

THIS PLANE IS CALLED THE ECLIPTIC.

THE EARTH SPINS ABOUT ITS OWN AXES

AND THE AXIS OF ROTATION IS AT A 23 DEGREE ANGLE

RELATIVE TO THE ECLIPTIC.

ACCORDING TO KEPLER'S LAWS, THE EARTH'S ORBIT IS AN

ELLIPSE WITH THE SUN AT ONE OF THE FOCI OF THE ELLIPSE.

SUPPOSE IT TAKES TIME (T1) FOR THE EARTH TO GO

FROM THIS POINT IN ITS ORBIT TO THIS POINT.

LET'S DEFINE AREA 1 AS THE PORTION OF THE ECLIPTIC

THAT INCLUDES PART OF THE ORBIT

AND THE CORRESPONDING AREA OF THE ELLIPSE.

LET'S DO THE SAME FOR TIME (T2) AND AREA 2

AT A DIFFERENT PART OF THE ORBIT.

ACCORDING TO KEPLER, IF T1 AND T2 ARE EQUAL

TO EACH OTHER, THEN SO ARE AREA 1 AND AREA 2.

AS YOU CAN SEE, MANY REAL-WORLD PROBLEMS

INVOLVE A KNOWLEDGE OF BASIC GEOMETRIC FIGURES.

IN THIS CASE ANGLES AND PLANES.

NOT ONLY THAT, IT'S IMPORTANT TO KNOW THE

PROPERTIES OF ANGLES AND PLANES IN ORDER TO USE YOUR

KNOWLEDGE OF GEOMETRY TO SOLVE REAL WORLD PROBLEMS.

IN THIS PROGRAM YOU WILL EXPLORE

THE FOLLOWING CONCEPTS: