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M4.4.6

Estimates the effects of measurement errors on calculations.

Estimating Planar Areas Using Analogue Methods

A method to estimate planar areas for simple or complex shapes is described. The method relies on the use of weighing the area of interest and using proportional constructs.

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When a Ruler Is Too Short

Surveyors are often seen in the middle of the street making careful measurements of angles with their transits, and distances with their steel tapes. For points than can be easily reached, such a survey is convenient. But when the target is inaccessible – a mountain summit or a distant star – known distances can be combined with measured angles to determine a distance or altitude. The method relies on parallax, the way an object appears to move, relative to a more distant background, when viewed from different angles.

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What the Doppler Effect Tells Us About Distant Stars and Planets

Police officers, air traffic controllers, and astronomers all use the Doppler Effect to determine the speed of an object as it approaches or recedes from their radars or telescopes. The frequency (or pitch, for sound) of waves coming from a moving object is changed an amount directly proportional to the speed of approach or recession. The effect of the change, to raise or lower the frequency, specifically indicates that the source is approaching or receding, respectively.

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Seeing Interference Fringes

Demonstrate the wave nature of light by projecting interference patterns. Detecting the interference of waves is one of the most powerful methods in science for measuring wave phenomena, and using the waves and their interference can reveal underlying details of their sources and the materials through which they travel.

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Length of the Day

The length of the day is something we take for granted. Yet, much can be learned about the day -- and the way the Earth moves -- from careful observations of the Sun and a more distant star, over as little as 24 hours, with a home-made viewer and a good clock.

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Learning from Slide Rules

In the days before calculators and personal computers an engineer always had a slide rule nearby. These days it is difficult to locate a slide rule outside of a museum.

I don't know how many of those who have used a slide rule ever thought of it as an analog computer, but that is really what it is. As such, the slide rule can be used to teach the modern view of the relationship between nature and mathematics and about the formalization of this concept known as isomorphism, which is one of the most pervasive and important concepts in mathematics.

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