Real life

Area of a Plot of Land

The last four posts dealt with formulas for finding areas using lengths of sides, starting with the triangle, where that is all you need, and then quadrilaterals, where something more must be added; and then using coordinates of vertices. Now we can use those tools to solve some of the more common real-life problems we …

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Complicating the Converse

(An archive question of the week) Usually when we discuss converses (and inverses and contrapositives) we use clear, idealized examples. But statements in real life — even in real math — are not quite so straightforward. The difficulty is not merely in the language, but in the complexity of our statements. A question in the …

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Significant Digits: Measurements and Exact Numbers

To conclude this series on significant digits, I want to look at some details of their application. Specifically, we will consider questions about how they related to measured values, and to fixed constants. Measured values I’ll start with a question from 2011 about measurement and unit conversion: Changing Units … and Significant Figures? Suppose I …

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Significant Digits: Operations

Last time, we introduced what we mean by significant digits (or figures), and touched on why they are defined as they are. Here we will look at how significant digits and decimal places differ, and how they are affected by operations (primarily addition and multiplication). This is another aspect of why they are defined at …

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A Tank with a Conical End

(An archive question of the week) Last time I surveyed what we have said about the volume of liquid in various kinds of tanks. One more special case I ran across deserved more detailed attention, because it demonstrates in detail how to do the calculations without much knowledge of calculus. The problem Here is the …

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