So how big does the inner circle need to be in order to put those four points on one straight line?
It turns out to be about 38%. But this is math. We want to know exactly how much and we want to know how to find the answer!
Let's consider the bigger circle a unit circle, so R = 1. Then consider this triangle.
Ten equal sectors define the entire 360°, so they're 36° each. The center-touching angle of this triangle encompasses 2 of those sectors. Therefore, 72°.
Unfortunately, I have to use cosines now. Those who fear trigonometry may want to look away.
Cosine equals adjacent over hypotenuse. We defined the hypotenuse to be 1, because it's a unit circle. So the cosine of 72° is the height of that triangle divided by one. Or just the height of that triangle.
h = cos 72°
Now lets look at this slightly different triangle.
That's only 1 out of 10 equal sectors that make up the entire circle. That's a 36° angle. And the cosine of that one is the height of the triangle (the same as the other triangle) divided by the radius of the inner circle — exactly we're trying to find!
cos 36° = h / r
But we know what h is.
cos 36° = cos 72° / r
Now we solve for r.
r⋅ cos 36° = cos 72°
r = cos 72° / cos 36°
That's the exact answer: cos 72° / cos 36°
If you throw it into a calculator, you'll get something like
≈ 0.3819660112510519363...
Like I said, about 38%. Or 38.197%, if you want to be pedantic. Which I hope you do.
And if you don't want your stars straight... that's fine, too. Every star is perfect for someone. ❤️🧡💛💚💙💜
In theory, Annabeth Chase is the responsible, mostly level-headed, no-nonsense member of the Seven.
In practice, Annabeth Chase is a math-obsessed ADHD girl that's been training to fight for her life since she was seven, has fought in two (2) wars by the time she turns seventeen, and is simply Too Tired™ to care about consequences of her impulsive thoughts, if she ever did.
What I'm saying is she pitches the dumbest hypotheticals to Leo and then they hole themselves up with limited food and sleep to try the idea out, no matter how stupid. Their cabins often join, sometimes others as well. It's a bit like MythBusters but with less regard for human life and even more explosions. Chiron and Mr D know Something Is Up if they haven't seen either of the two in too long.
Okay hear me out. What if Hornblower and Lady Barbara but they're high school math olympians and also have a crazy psychosexual rivalry with each other
In the 90s, many of the games that CJ appeared in took place at different points in time, from a modern day school in JumpStart 2nd Grade, to medieval times in JumpStart Math for Second Graders, to a prehistoric era in JumpStart Spelling (top). Then in 2001, JumpStart Explorers depicted CJ as owning a time machine (bottom), which could retroactively explain his various time leaps in earlier games.
lil height comparison chart for shits n giggles but now with big fat noodle edition based off the moonchase cutscene instead of his fake dead noodle form
Y’all ever heard of the Chicken McNugget Theorem? Also known as the McNugget factor?Y’all know what the largest number is for which it’s impossible to buy exactly that number of McNuggets? It’s 43 incase you were wondering. Can’t buy exactly 43 Chicken McNuggets.
I also made an animation with pause and play buttons here. Reload that page to see it calculate the square root of a different pseudorandom number.
I had planned to make a slideshow that walked the audience through the process step by step, but it was over 20 slides, too much text, and just... a lot. If you want to see that, it's here.
Vickie Bottelson, the lead vocalist for the theme songs of JumpStart Advanced Preschool/Kindergarten, also provided the lead vocals for the Math Blaster theme song around this time.