Yes, we are doing math! After Science, then a little bit Science and History, then English, now we have some math t0 do! Okay, if that title made zero sense to you, well you’re not alone. Math may seem hard, confusing, and ridiculous at first, but eventually you’ll get the gist of it.
Okay! First, counting 1+2+3+…+n super quickly. In that statement, “…” means basically all the numbers between (in this case) 3 and n. So for example, you could have 1+2+3+4+5+6, where in this formula, the n equals 6.
Oh, we haven’t gotten to the formula yet? Here it is:
yes I know it looks really confusing but the point is this, 1+2+3+…+n is always n(n+1) divided by 2. So, if like in our previous example, n=6, it’ll be 6 * 7 / 2. Which is 21, and if you try to check it using the normal boring slow method, it’ll be correct.
This will work with any value of n, so if you would like to know 1+2+3+…+98+99+100, you know it’ll be 100 * 101 / 2, which is is 5050. Not really that hard when you’ve got the formula right?
Okay, next one! This one’s a little bit harder but the key is always logic, and most of the time requires a formula. Here we go! Imagine three equal-sized circles inscribed/circumscribed/tightly packed into an equilateral triangle. Each of the circle has a radius of 1 cm. Now, try to find the perimeter of this triangle:
So, let’s start by first making a small triangle at the corner:
Okay, so how did I find these angles? Simple. The bigger triangle is equilateral, so each angle is 60°, and now we’ve halved it. 30°. Next how did I get the 60°? Obviously the other angle is a right angle (90°), so then 180-30-90=60°. Understand so far?
Alright, now we reach the formula part. For every 30-60-90 triangle, there’s a formula to find out their sides:
So well yeah. Just put in the radius, which is 1 in this case, into a, and boom. We’ve got all the side lengths. The rest is easy.
So yeah. The rest of the side is just the radii of the circle, 1 cm each, so for every side it’s 2 + 2 √3 cm and so for the perimeter, it’s just (2 + 2 √3 cm) * 3 = 6 + 6 √3 cm!
Okay, so today we finished two pretty hard-looking but essentially easy enough (with the formula) questions. How did you feel about this week’s Weekend Lessons? Leave your comments below and have a good day!
Ryan's Brain 