Stupid Math Tricks Jan 18 2012 - Stupid Math Tricks d = 1/p...

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Stupid Math Tricks! E=mc 2 d = 1/p P 2 = A 3 P 2 = A 3 Yo, Prof., is this gunna be on the exam?
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D St d t Dear Students, This is a compendium of ppt slides from previous math examples that have been presented in class at various times. I will try to update this on occasion, so look for the date in the file name in Bb to see if it is new or not. In the first part are basic examples that could appear on an In the first part, are basic examples that could appear on an exam. In the second part presents responses to questions I have gotten from students and/or other in depth background treatments of the material.
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Significant figures. Rule of Thumb: A number that is accurate to 1 % is ok for this course In general take the first four non zero A number that is accurate to 1 % is ok for this course. In general, take the first four non zero numbers to the left, and round of f the fourth number to make three significant figures: So, for π = 3.14159265358979323846264338327950288419716939937510582……… We can take 3.141 and round to make it 3.14 For 66.739, we would make it 66.73 and round to 66.7 For 0.01596473894, we would make it 0.01596 and round to 0.0160 . For 1,356,786.333, we could either round to 1,360,000, OR, we could write 1.36 x 10 6 Exceptions to the rule! If two numbers are very very close to each other, then one must keep enough places so that when they are the answer, or are used in a calculation, you keep enough places so you don’t send the baby down the drain with the bathwater: places so you don t send the baby down the drain with the bathwater: If A = 1.023462769 and B = 1.023462768, Then if you round, then A = B = 1.02, and A B = 0. But, if you first subtract them, then A B = 0.000000001 = 1 x 10 9 which is significant!
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Some Magic Angles: A l di t f th M d th S f E th 0 5 0 Angular diameter of the Moon and the Sun from Earth: 0.5 Tilt of the Moon’s orbit out of the ecliptic: 5 0 Tilt of the Earth’s rotation axis out of the ecliptic: 23.5 0 Tilt of the ecliptic plane out of the Galactic plane: 63 0 Lagrangian points (for the Trojan Asteroids, etc.): 60 0 Amanda Hamilton π ( 3.14 radians): 180 0 One arcsecond: 1/3600 0 One radian: 57 0 One arcsecond: 4 85 x 10 6 radians One degree: 0.0175 radians Maximum angular If a 1 cm grape has an angular size of one arc second, how far away is it? i i l Si (i di !) 4.85 x 10 Milli arcsecond (MAS): 4.85 x 10 9 radians distance of Venus 47 o and Mercury 28 o from the sun. Diameter = Distance x Angular Size (in radians!), so Distance = 1 cm/4.85 x 10 6 = 2.06 km or 1.3 miles. How about an angular size of one MAS? Distance = 1300 miles. Easy for large telescopes!
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Common units and expressions used in our class: λ . The wavelength λ of light (and also the size of many other objects) is very often given in many different units, based on who the scientist is. Usually, you want to use units so that the number you are dealing with doesn’t have too many zeros to the right or to the left of the decimal point. Usually, the units are in multiples of a thousand, except for centimeters.
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