<p>@StanfordWOW Its diameter will be a lot smaller than the diameter of the circle.</p>
<p>I’m making a new google docs…</p>
<p>What is up with the last one? Make it open to everyone, please.</p>
<p>Also I multiplied everything out for the ones digit question and i got 6. Not sure if i made a mistake typing it all in</p>
<p>Huh, I don’t know, I checked everything and came up with that giant number above.</p>
<p>Oh crap I was missing the 4. Yup, it’s 6.</p>
<p>What do you mean “missing the four”?</p>
<p><a href=“https://docs.google.com/document/d/1hlrbubFeQrQFrJDGb6Ml1SJtCwb_You2DJK8d6j2d8w/edit?usp=sharing”>https://docs.google.com/document/d/1hlrbubFeQrQFrJDGb6Ml1SJtCwb_You2DJK8d6j2d8w/edit?usp=sharing</a></p>
<p>@mrnephew @BassGuitar the question was how many great circles can you draw that connect points A and B. It defined a great circle as a circle within the sphere with the same diameter as a sphere. </p>
<p>Think about it this way. lets say you had an orange and marked any two points, A and B, on the surface of the orange, and aligned a knife through both points and sliced the orange and half along the line. You would get a great circle… It’s diameter is equal to that of the whole orange, and it passes through both A and B. </p>
<p>I got tripped up at first as well, but you have to sorta think about it…</p>
<p>For great circles I put more than 3 cause I thought B could be on any great circle of the sphere. But wa the question only putting B on that one circle that was drawn?</p>
<p>Exactly. And by that definition, since A and B were on the same hemisphere of the sphere, circle AB’s diameter was not the same as the sphere’s.</p>
<p>@mrnephew ??? go get a knife, sharpie, and orange right now. Label points A and B, line your knife up along points A and B, and cut it down the middle. You WILL get a great circle. Trust me…</p>
<p>going off the orange analogy, wouldn’t slicing the orange only yield a great circle if you cut through the center of the sphere/orange? and then if you cut through the center, you wouldn’t be able to include both points a and b, which is why i put 0</p>
<p>@mrnephew @BassGuitar let’s visit the definition of a great circle again then… A great circle is defined as a circle whose DIAMETER is the same as the DIAMETER of the sphere. Yes, the chord connecting A and B are NOT equal to the diameter, but the circle that connects A and B within the sphere has a DIAMETER that IS EQUAL to the DIAMETER of the sphere. </p>
<p>THEREFORE, there is ONE such great circle that CONNECTS A AND B.</p>
<p>For any two points on the surface of a sphere there is a unique great circle through the two points
<a href=“Great circle - Wikipedia”>http://en.m.wikipedia.org/wiki/Great_circle</a></p>
<p>Definetely 1</p>
<p>@vivalamelanie ok, I can see what’s confusing, but I don’t know how else to explain it. If you really want to understand, get up RIGHT NOW get a SHARPIE, KNIFE, and an ORANGE and mark points A and B. Then CUT THE ORANGE IN HALF BY LINING UP YOUR KNIFE WITH POINTS A AND B… </p>
<p>:( why is this so hard to get…</p>
<p>^ okay then its 1. thank you for settling that</p>
<p>hehe sorry @StanfordWOW </p>
<p>wait y’all how many x intercepts were there, none or 1?</p>
<p>@vivalamelanie but you get the logic behind it, right? I’m notorious for being bad at explaining things to others, so sorry if you still don’t get it. </p>
<p>Like I said though, if you want to understand my logic, actually go get an orange XD…</p>