Another Dream in Which I Seemed to Know Some Fact I Had Never Learned

 In my previous post "Can You Know in a Dream Some Fact You Never Learned When Awake?" I discuss two interesting cases in which I seemed to know something in a dream that I had never previously learned while awake.  In one of the dreams Betty White rejected a romantic overture from Allen Ludden, something that happened in real life, but I had not learned about before having the dream. (The two eventually married.)  In another dream someone seemed to know that a marmoset was a tree dweller, even though at the time I had the dream I did not know this fact, and could not even identify what a marmoset was upon waking from the dream.  This morning I had a similar dream of this type. I seemed to know in the dream that pi (the ratio of the circumference and the diameter of a circle) is important in solving a particular problem, although I did not know this fact before the dream.

 It is an interesting brain teaser to ask someone how he would compute the area of a rectangle with a large hole in its center, one looking like the figure below. 

You can ask a person: "Suppose you know the radius of the circle, and the width and length of the rectangle. And suppose you have an internet connection. How would you compute as quickly as possible the area of the green shape?"

The answer is:

(1) First, you use the Internet to very quickly find the formula for computing the area of a circle, which is "area = pi times radius squared,"  and use that to compute the area of the circular hole. 

(2) Then you compute the area of the green rectangle, by multiplying its width by its length. 

(3) Then you subtract the first number from the second to get the area of the green figure. 

In my dream of this morning, I was with people who were trying to solve this problem. In the dream I said to someone, "You'll probably end up using pi." That was correct. Pi (the ratio of the circumference of a circle to its diameter) is part of the correct solution of this problem. But how did I know this in my dream, having never previously pondered this problem, and certainly not knowing the formula for computing the area of a circle? The dream is one of many I have had that collectively bolster my belief (held mainly for other reasons) that dreams do not come from brains, and that dreams sometimes have a source beyond individual human minds.  My reasons for doubting that mental phenomena come from brains are discussed in the posts of my blog here.