Daniel R Hicks
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 Aug 7 comment When has one sufficiently mastered an area of mathematics? When you can present a concise mathematical model of the English language. Jun 7 comment How to generate a random number between 1 and 10 with a six-sided die? Simplest is to roll the die twice (or roll two of them). Add the first value and 6 times the second value. If the result is greater than 10, discard the result and try again. A modification to produce fewer discards is to produce your sum, then, if it's < 10 & <= 20, subtract 10, < 20 & <= 30 subtract 20, < 30 discard. May 11 comment Why are two planes parallel to the same line not necessarily parallel? Two planes that intersect are both parallel to the line of intersection. Mar 6 comment What is an odd prime? OK, things are getting too odd in here -- I'm leaving! Dec 8 comment Simple paper cuts problem Seems to me that the easiest way to prove that it's #4 is to just get scissors and paper and try it. Nov 24 comment Will it become impossible to learn math? You can always just keep making the specialties narrower and narrower, but, practically speaking, the ability for one person to "understand math" was probably lost 100 years ago. The problem is not simply memorizing material, but truly understanding the concepts of geometry, calculus, game theory, cryptology, probability, chaos theory, field theory, quantum mechanics, and a hundred others. It is beyond the abilities of any mere mortal. Nov 1 comment Why are there letters as additional digits in bases greater than the decimal base (10)? Some "seven-segment" displays are capable of displaying digit values 10-15 as combinations of the segments that do not make valid decimal digits. Eg, U, upside-down 7, upside-down U, backwards 3, etc. Nov 1 comment Why are there letters as additional digits in bases greater than the decimal base (10)? @dbmag9 - Base 100 is significant because some (old) system use(d) "centesimal" notation internally, with values between 0 and 99 stored in each "digit". Oct 31 comment Problem on selecting group of card from a well shuffled pack of card Understand that this is not a statistics problem, since you have to guarantee an outcome. Ie, you need to figure out the worst case. Oct 16 comment A 1,400 years old approximation to the sine function by Mahabhaskariya of Bhaskara I Except that that formula requires performing fractional exponents, so arguably not simpler. Oct 16 comment A 1,400 years old approximation to the sine function by Mahabhaskariya of Bhaskara I Yeah, Indians cooked up some pretty good pi back in that era. Oct 8 comment Do mathematicians, in the end, always agree? @Bakuriu - I'd say it's completely not allmost. Oct 3 comment Prove that a logarithm is irrational Prove?? Heck, I've known they were irrational ever since Mr Jesse first talked about them! Oct 1 comment Google Interview Question about a town where if a couple has a girl born, they can't have more children… @ReneSchipperus - I've never read anything "hard" on the topic, but I've seen several discussions of the genetic and environmental factors that influence the sex of the infant. Oct 1 comment Google Interview Question about a town where if a couple has a girl born, they can't have more children… I'm sure it can be shown that in "real life" sequential births from the same parents are not "independent". There are subtle effects that will tend to cause parents of girls to produce more girls and parents of boys to produce more boys. Also, the ratio is not exactly 1:1. So one must ask: Are we talking "real life" or an idealized/theoretical scenario? Sep 24 awarded Autobiographer Aug 27 comment What is the average of no numbers? Consider that the average of { 17539126 } is 17539126. And the average of { 17539126 , 2 } is 8769564. If the average of { } is considered to be zero, wouldn't you expect that to "pull down" the average of the lists of 1 and 2 elements? Jul 26 comment What are some conceptualizations that work in mathematics but are not strictly true? Mathematicians are really sexy. Jul 2 awarded Curious May 26 comment Can the square root of a real number be negative? It appears to me that a part of the "problem" here is that the square root operation is relatively unusual in that it denotes the solution to an equation, whereas the vast majority of mathematical operations (at least the more familiar ones) do not. It's perfectly legitimate/un-scary for an equation to have multiple solutions, but we do not normally expect operators such as monadic - to produce multiple contradictory values. Thus there is some cognitive dissonance with the square root operator.