How Math Can Save Your Life

That’s precisely the rule that generates the sequence 1,3,7,15,31, ... Each number is twice the preceding number plus one, and each number is also one less than the appropriate power of 2.

Show the pattern 1,3,7 to a mathematician, and he or she will notice that each number is 1 less than the next power of 2:1 is 1 less than 2, 3 is 1 less than 4, and 7 is 1 less than 8. He or she will then conjecture that it takes 264—1 moves to transfer 64 disks.

The primary purpose of division is to share a number of items as equally as possible.

That year the Tulip Index stood at 6.39, which means that the S&P had appreciated more than six times as rapidly as annual income since 1975.

Cash that sits in a bank vault does not make money for a bank; the bank makes money by making loans

The “Bradley effect,” named after Thomas Bradley, a former mayor of Los Angeles, was discovered when Bradley lost the 1982 California gubernatorial race after being ahead in the polls. It was conjectured that white voters may have stated to pollsters that they intended to vote for Bradley, an African American, in order to avoid being stigmatized as racist, when in actuality they intended to vote for Bradley’s opponent.

a score of 85 is 8 points above the mean of 77. Because a standard deviation for that distribution was 4 points, 8 points is 2 standard deviations, and the score of 85 can be expressed as being 2 standard deviations above the mean.

tightly packed the data are around the mean.

the mean, which is a measure of the middle score of the distribution, and the standard deviation, which is a measure of how

It may indeed be a good move for you to refinance, but you must understand one very important fact: you are not saving $175,000, you are making $175,000 less in payments. It may seem like the same thing, but there’s a very important difference, and in order to appreciate what’s happening, we need once again to compute present value.