The GG Network blog — page 19
Free lessons that leave you a little sharper every visit — plus deep guides to the professional tools. Knowledge shouldn't sit behind a paywall.
Area grows with the square of the radius, which makes the difference between two round things much larger than their diameters suggest. Worked through with real numbers, including the two-small-versus-one-large comparison.
The right-triangle relationship earns its keep away from the classroom: sizing a diagonal brace, checking whether something fits through an opening, and proving a corner is square before you fix it.
What you want to earn and what you have to charge are separated by holiday, unbilled hours, premises, insurance and every job you quoted for and did not get. The gap is bigger than almost anyone guesses.
The same percentages applied in a different order produce different money. Here are both orders on identical figures, and why only the agreement can say which one is right.
Freight, duty, handling and the exchange spread all land on the same box of goods. A product that looked profitable on the invoice can be a loss by the time it is on the shelf.
You buy a kilo and you serve 800 grams of it. Cost the dish on what you bought, not on what reached the plate, and every price on the menu is quietly wrong.
A pseudo-random generator given the same starting value produces the same numbers forever. That is a feature and a limitation, and knowing which is which decides what you can use it for.
One die is even across all six faces. Two dice are a triangle peaking at 7, and 7 comes up six times as often as 2. Here is every outcome, counted.
Two machines that have never spoken can each invent an identifier and be confident they do not clash. The confidence comes from arithmetic, and the honest word is negligible — not zero.
The obvious way to shuffle a list is subtly wrong, and you can prove it by counting. Here are all 27 outcomes for a three-name list, and what the correct version changes.
One skewed set can have an average of 17.78 and an average of 5 at the same time, both correct. Here is how to tell which one you have been handed.
Two group averages of 80 and 50 do not make 65 if the groups are different sizes. Here is the worked example where the two methods disagree by nine points.