## Math: golden ratio, first glance

Tutoring math, you see the golden ratio. The tutor mentions it. There are a few peculiarities that explain the golden ratio’s uniqueness. Let’s call it r. Then for a number x, x/r = x(r-1). r is irrational; an approximation is …

## Math: inverse trig functions in Chrome

Tutoring math, modern facilities are always interesting. The tutor mentions the Chrome browser. The Chrome browser is useful for inverse trig functions. Suppose, for instance, you know that tan of an angle is 1.5 but you want to find the …

## Math: sin in Firefox Google Search

Tutoring math, angles in different measures come up. The tutor mentions the Google Search Bar for sin. Most people familiar with sin probably expect the result 0.5 for sin30°. Tonight, in the Google Search Bar on Firebox, I keyed in …

## Math: what is mensuration?

Tutoring math, terms arise. The tutor mentions mensuration. Mensuration means determining quantities that can’t be measured directly from ones that can. Basic measurements or observations, arrived at using a measuring tool such as a ruler, protractor, watch, etc, are input …

## Math, physics: decibels: a practical example

Tutoring math, everyday situations come up. The tutor mentions a construction application: noise dampening. Today I was at a hardware store and noticed some ear protection rated as reducing noise by 27 decibels (aka 27 dB). What amount of noise …

## Probability: real vs observed

Self-tutoring about probability: the tutor gets (perhaps) philosophical as well. Is the real probability of an event calculable from theory? First, let’s imagine tossing a coin. Theoretically, its probability of heads is 0.5 – tails, also 0.5. Let’s say you …

## Math: the optimal stopping problem

Self-tutoring about math in everyday life: the tutor mentions a gem. Even among people who avoid math, it’s hard to imagine one who doesn’t engage in the optimal stopping problem. The optimal stopping problem means deciding when to choose an …

## Financial math: calculation of mortgage interest rate

Self-tutoring about financial math: the tutor mentions the mortgage interest rate. I was looking at the formula for the periodic payment of a mortgage: P=(-1(r/n))*L*(1+r/n)^(nt)/(1-(1+r/n)^(nt)) where P=payment r=rate n=payments per year (and compounding periods per year as well) t=years Specifically …

## Math: Pythagorean triples and Fermat’s Last Theorem

Tutoring math, ideas are always important. The tutor mentions Fermat’s Last Theorem. A Pythagorean triple is a set of three integers that satisfy a2+b2=c2 There are infinite Pythagorean triples. However, there are no corresponding sets of integers for higher n: …

## Math: set subtraction

Tutoring math, ideas can always be revisited. The tutor mentions set subtraction. Set subtraction is different from arithmetic subtraction. If A and B are sets, the operation A-B ignores what’s in B only; it just gives back what’s present in …