Maths (math) people of the US: I need your help in working out if certain British conventions would be understood or standard in the US classroom.
I'm working on some text that will be read by schoolkids in the US. There is a fair bit of math involved, and while I'm confident I've "translated" most of it properly there are a few things I'm not sure about:
1. "The formula that describes the steps can be applied to find any triangular number, where T(n) is the sum of the numbers from one to n"
Is T(n) correct in the US here?
2. "Firstly, Newton developed differential calculus, a method for calculating the gradient of a curve on a graph."
Should "gradient" be "slope" here?
3. Vectors/coordinates. I have the sentence "To calculate the vector that describes the movement of an object between two points, like an aeroplane, the coordinates at point A are subtracted from point B" illustrated with something like:
B(2, 10, 4) - A(5,0,5) = AB (-3,10,-1)
except that there the numbers in the parantheses are piled on top of each other rather than being separated by commas, as in the numerous examples in this link
there is a right-facing arrow above "AB"
Is this how this should be presented in the US?
4. "The gradient of a straight line is calculated by dividing the change in vertical height by the change in horizontal distance. At first, the flat ocean bed has a zero gradient – there is no slope at all. Despite moving only a few millimeters each year, folds develop over time, and a slight gradient of 0.1, or 10%, builds up. Over millions of years the fold mountain continues to grow and, as the gradient gets steeper, it rises above sea level. "
Again, should all of these "gradient"s be "slope"s? Or should they be "grade"s, because we're talking about mountains? Or a mix of the two?
Thanks for your help!