By P. Ciarlet

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**Extra resources for An Intro. to Differential Geometry With Applns to Elasticity**

**Sample text**

Joe: I knew we were relying too much on these coincidences. My guess is that these “rules” don’t always actually work! Jill: I really don’t think that’s what it means. … What do you think it means? Com it’s not really a straight line If it doesn’t all add up, then something isn’t as it seems The mystery angle is 18º and the mystery angle is 13º…well, that clearly doesn’t add up. If the mystery angle is 13º, then it can’t be vertically opposite our 18º bullet path angle as well. This means that the line on the sketch from Benny to Micky doesn’t join up perfectly with the bullet path.

You can assume that all the lines shown here are straight. We know that you can always fit a pair of right angles on a straight line, but what if we don’t have right angles? What might this pair of mystery angles (a and b) from our crime scene sketch add up to? Com lining up Solution We know that you can always fit a pair of right angles on a straight line, but what if we don’t have right angles? What might this pair of mystery angles (a and b) from our crime scene sketch add up to? 9º 81º aº If we had a pair of right angles, they would add up to 90º + 90º = 180º.

What we need to find out is whether they join up to form one single straight line. Com finding missing angles Complementary angles always add up to a right angle (90º) If two angles combine to creat a right angle we call them complementary angles. Usually, complementary angles are adjacent (next to each other), but they can be any two angles anywhere that add up to 90 degrees. Hey, you look nice today! Thanks! Not so bad yourself.... We say that the angles complement each other. 72º 18º 18º + 72º = 90º so these angles are complementary.

### An Intro. to Differential Geometry With Applns to Elasticity by P. Ciarlet

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