The Physical World

The Physical World includes applications of many different mathematical topics to geography, geology, astronomy, and physics, optics, and projectile motion.
Studying various physical aspects of geography can involve the use of angles and angle measurement, area and area measurement, ratio and proportion, statistical analysis of data, and coordinate graphing to identify map locations. 

  • Is Central Park warming?  
  • What is the relationship between latitude and temperature?  
  • What creates the seasons of the year?  
  • How can students use maps to compare the areas of states in the U.S.?

Geology presents opportunities to use mathematical functions, scale measurements, ratio and proportion, coordinate graphing on maps, and modeling in three dimensions. 

  • How can linear and nonlinear functions be used in studying arches in Utah’s Arches National Park? 
  • How can depths of the seafloor be determined for different locations?  How can a model be constructed for a section of the seafloor?

Astronomy has fascinated humans from ancient times to the present.  Topics from geometry and trigonometry are essential in exploring aspects of astronomy. 

  • What is solar noon and how can solar noon be calculated?  
  • What are important characteristics of planetary motion?  How can the period of a planet be calculated?  Or the eccentricity of its orbit?

A variety of mathematical topics are required to study phenomena from physics, optics, and projectile motion. 

  • What physical and mathematical properties of parabolic mirrors are involved in the design and use of telescopes that focus light from distant objects?  Properties of parabolas, coordinate geometry, and trigonometry are indispensible in studying telescope optics. 
  • What kinds of mathematics are needed to analyze the motion of a golf ball propelled by a launching device?  Geometry, trigonometry, and algebraic functions form the basis of the investigation.  
  • Why does a stream of water from a fountain follow a parabolic trajectory?  Quadratic functions, properties of parabolas, and projectile motion under the influence gravity help to explain why.