Geometry
Whether you’re interested in measuring a bridge or exploring the intricate designs of nature, geometry offers tools to make sense of the shapes around us. By learning to use theorems--which help us make different types of calculations--geometry can help in our daily lives and is an important part of such varied fields as engineering, navigation and even art. Explore geometry by delving into its history, learning how to apply its theories and exploring its beauty through fractals and tesselations through the direct links on the Times Launch Point Web site: https://www.latimes.com/launchpoint.
Level 1
Hawaiian Geometry: Discover shapes in the world around you through these photos that spotlight circles, cones, polygons and more through photos of Hawaii. Get acquainted with aspects of Hawaiian culture as you explore geometric figures and learn about symmetry.
https://kalama.doe.hawaii.edu/hern95/rt015/geo/
Exploring the Shapes: What is the difference between a trapezoid and a rhombus? Try some online exercises in which you identify and compare shapes.
https://math.rice.edu/~lanius/Patterns/
Fantastic Fractals: Fractal geometry helps us to understand the complex shapes found in nature, such as fern leaves and clouds. Learn about the unique shapes of fractals through animations and exercises as well as examples of fractal music and fractal landscapes.
https://hyperion.advanced.org/12740/netscape/forkids/page2.html
Level 2
Interactive Math Lessons: The distance around a circle is called its circumference, while the distance across a circle is its diameter. Learn about measuring shapes through the online geometry lessons “Circumference & Area of Circles” and “Perimeter & Area of Polygons.”
https://www.mathgoodies.com/lessons/
Polyominoes: How are polyominoes like the games of dominoes or Tetris? Find out about this special class of geometric figures through some colorful exercises.
https://math.rice.edu/~lanius/Lessons/Polys/poly1.html
Ptolemy’s Tools: Explore geometry outdoors through such activities as finding out how to measure the height of a rocket’s flight or how to triangulate the distance across a river. Learn about the history of the quadrant and how this tool has helped people make complex measurements.
https://library.advanced.org/19029/quadprojects.htm
Level 3
Geometry: Points are zero-dimensional, which means they have no height, length or width. Learn about geometry’s main postulates and theorems, find out how to understand proofs, and make use of sample problems and a huge glossary.
https://tqd.advanced.org/2647/geometry/geometry.htm
Geometry Online: The history of geometry begins with the ancient Egyptians, who used it in surveying and construction, and continues with the ancient Greeks, who with Euclid’s book “The Elements” laid the foundation for all future studies of geometry. Explore the history of geometry, try some exercises with impossible triangles and the golden ratio, and test your knowledge with an SAT-type quiz.
https://math.rice.edu/~lanius/Geom/
Totally Tessellated!: Tessellations are repeating patterns of interlocking shapes. Learn about the mathematics behind these patterns made famous by artist M.C. Escher, view tessellations from various cultures and try your hand at making your own math art masterpieces.
https://library.advanced.org/16661/
EXPLORER’S QUEST
The answer to this Internet quiz can be found in the sites at right.
What ancient navigational tool relied upon the geometrical concept of the quadrant?
CLUE: See Ptolemy’s Ptools
Find What You Need to Know: Have a project on California history? Need help doing a math problem? Launch Point now covers more than 100 topics for getting your schoolwork done. Go to https://www.latimes.com/launchpoint/ for the full list of subjects and direct links to the best Internet sites.
Answer to last week’s Quest: Interchangeable parts meant that products could be assembled and repaired quickly.
Launch Point is produced by the UC Irvine department of education, which reviews each site for appropriateness and quality. Even so, parents should supervise their children’s use of the Internet. This column was designed by Jennifer Olenicoff, Jessica Pohle, Jean Hong and Anna Manring.