Math things I should have realized earlier

I learned both ways in the late 60s. I prefer the one I used up tread (left to right?), as it makes the most sense to me.

An easy way to estimate annual income is hourly rate x 2000. That is, rate x 40 hour week x 50 week year (assume 2 weeks unpaid vacation to keep the number easy) = x 2000.

So $15 an hour equals $30,000 annually, ($15 x 2000), $55 an hour equals $110,000. If multiplying by 2000 seems unwieldy, remember you’re just multiplying the hourly rate by 2 (ie doubling it), then multiplying by 1000 (ie adding 3 zeroes). So a $9 minimum wage would be 9 doubled, or 18, with 3 zeroes: $18,000 annual salary.

I have a houseguest right now - family bunking here while they get their financial shit together - and the 20-year-old is enrolled in a technical college certificate program designed in conjunction with Gulfstream Aerospace to train potential employees in aircraft manufacturing. The kid is making okay grades, but it’s very, very clear that he’s just grinding away trying to memorize things, and has absolutely zero understanding of the concepts he’s learning.

The math thing that I apparently should have realized sooner? Some folks don’t realize that math is simply logic spoken in numbers and variables instead of words. And that most math and geometry has practical applications in every day life. Seriously, tonight’s homework was review for an upcoming test - converting units of measurement from Imperial to metric, or between different units of one system (feet to miles, liters to gallons, inches to millimeters, etc.:wink: finding area and volume of basic shapes; converting fractions to decimals and vice versa; and figuring proportions. My daughter is in eighth grade, and was drawing upon sixth-grade math to help the Kid review. He’s clueless.

But, what really, really floored me: he had no concept that this was a skill set that he would actually need to master and use in order to build airplanes. He really thought that this class was like a core class required to get a liberal arts degree - something extra to provide breadth of knowledge, instead of just depth.

When I explained why one might actually need math skills to pursue a job in any construction or manufacturing trade, I almost made his head explode. And when I explained that we all use all sorts of math daily, that math wasn’t just a class one took to graduate high school? It was an entirely new concept to him! You use decimals every day - money being the most obvious example. As a housewife, I have to use fractions, convert units of measurement, and so forth all the time: I cook and bake, I figure out what kind of mileage my car gets, I estimate sums when I’m at the grocery store and have to stay within a budget, I figure cost per unit to see whether the big box of cereal is a better price than the two smaller boxes. When we were remodeling the house, I had to measure, convert, estimate all the time - figure how much paint to order, how many feet of flooring, and so forth.

My own “oh, duh” math moment happened very long ago, when I realized that liters could just as easily and accurately be described in cubic meters. It made perfect, logical sense, but I never thought about it until my first chemistry class (tenth grade, I guess?)

Other dude! Sorry!

Yeah, that crazy number nine. Times any number you can find, it all comes back to nine.

I just memorized a few Celsius temperatures, and can get by with that:
200°C = baking bread
100°C = boiling water
37° = normal body temp
20°C = room temp
0°C = freezing
-40° = forty below & darn cold in any scale!
From those I tell approximately what any Celsius temp is like.

But I really like your short version!

[speaking Canadian] Sorry. Ha ha ha. Sorry.[/Canadian]

If I posted that rule of thumb in Canadope Cafe we would all point and laugh at you. 10 is cold? Heh heh heh. I now live on the wet coast and have the most insufferable Schadenfreude* imaginable about weather in the Rest of Canada, but calling 10 degrees C “cold” only works in July. In some locations.

It is 12 C today, and while it isn’t “warm” outside by any means I will take it over the -12 in my hometown, but -12 is kind of a normal winter temperature. Maybe sucky for November, but in January we would all be feeling like “spring mighht be coming” at that weather.Temperature is very relative. And I will leave the cold weather back in my hometown with my relatives.

*Shadenfreude is very unCanadian, but the force is strong for people in Vancouver, while the Rest of Canada gets to point and laugh about our outrageous housing costs. 1.6 million dollars for a tear-down. What a bargain!

Very good. I just use rough and dirty .45 kg is aprox 1lb. People* seem to understand my kid was 10lbs better than 4500 grams, or even 9.9208 lbs. And 9lb, 15 oz doesn’t roll off my tounge as easily. But your estimate does give me 9.9 which is accurate.

(Elders, of the non metric generation. And my own age co-hort is confused: we learned imperial measurements for part of our schooling then the rest in metric by confused teachers with brand new textbooks.)

I “discovered” (I put it in quotes because I am sure that somebody must have found this a long, long time ago) a really nifty way to perform a rough conversion from miles to kilometers and back. Not precise at all, but good enough to get an idea of distances and speeds.

The ratio between miles and kilometers is 1 mile ≈ 1.609 km. Now, this number is “close” (for a certain value of close) to the golden ratio (φ≈1.618).

Remembering that the ratios of successive numbers in any generalized Fibonacci series tend towards φ, I made some checks and, hey, lo and behold – a generalized Fibonacci series will help you convert from miles to kilometers and back almost instantaneously, with a precision that is enough to give you a rough idea of the equivalence!

Let’s begin with the Fibonacci series itself, which gives us already in the beginning a very, very rough equivalence of miles and kilometers – 2 miles ≈ 3 km (actually 2 miles = 3.2187 km). Let’s build this series:

2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233…

According to my rule:

2 miles ≈ 3 km (actually 3.2187 km)
3 miles ≈ 5 km (actually 4.828 km)
5 miles ≈ 8 km (actually 8.0467 km)
8 miles ≈ 13 km (actually 12.8748 km)
13 miles ≈ 21 km (actually 20.9215 km)
21 miles ≈ 34 km (actually 33.7962 km)
34 miles ≈ 55 km (actually 54.7177 km)
55 miles ≈ 89 km (actually 88.5139 km)
89 miles ≈ 144 km (actually 143.232 km)
144 miles ≈ 233 km (actually 231.746 km)

As you can see the conversions hold within a few % of the real value, and generally give you a somewhat higher value than the real one.

By interpolating or beginning with a different set of values, we can get other conversions going. For instance, let’s imagine that we begin with “40 miles ≈ 65 km” (actually 64.3738 km):

40, 65, 105, 170, 275…


40 miles ≈ 65 km (actually 64.3738 km)
65 miles ≈ 105 km (actually 104.607 km)
105 miles ≈ 170 km (actually 168.981 km)
170 miles ≈ 275 km (actually 273.588 km)

To go from kilometers to miles, just follow the series in the opposite direction.

So, forget about precision, but if you want to have a rough-and-ready idea of how many km is a certain amount of miles (or the other way round), you can use Fibonacci-like series and (if needed) interpolation or multiplying by a given factor to find out :slight_smile:

For instance, how many kilometers are 90 miles? Well, from our set of series we know (roughly) how many kilometers are 40 miles and how many kilometers are 5 miles.

90 = 402 + 52.

So, if 40 miles are 65 km, and 5 miles are 8 km, we get that 90 miles should be:

652 + 82 = 130 + 16 = 146 km

Let’s check it out: According to Google, 90 miles = 144.841 km

Close enough for a rough estimation!