Hi Math Friends--
I found this chart interesting and wondered if anyone would like to join me in an exploration/chat regarding a pattern or rule.
I've tried a table of values and made some observations, but wish to push further and I thought a conversation would help.
Thank you for sharing this. I love thinking about how there were so many people necessary to create each one of us. We are all a mixture of so many people. It makes me think of fractions as well. I'm 1/2 my mother and 1/2 my father, who are each 1/2 of their mother and father. I'm 1/4 the grandmother I knew and 1/4 the grandmother I was too young to know. The number of ancestors grow exponentially and the fraction they each make up shrinks exponentially.
What did you notice in the table you made? What questions did it provoke? Is there something you want to answer for yourself related to the number of ancestors?
By the way, Mark and I used the example of ancestors to introduce exponents in math materials we wrote last year: Part 1, pg. 10-12 and Part 2, pgs. 24-27.
That is so cool! I'm happy to hear your feedback, and am going to pursue this exploration further..
Hello again, Eric--
I've been considering different ways of looking at the Ancestral Math progression, and have considered it in the context of fractions, as you'd mentioned. (I hadn't as yet looked up the lessons you provided, because I wanted to see what I could come up with on my own.)
I've tried a sort of table-chart in order to observe patterns, but am still curious as to how a graph or equation complement the situation(s). Now I'm going to check the links you sent.
I think it's great that you are exploring the phenomenon yourself. I'd love to see the charts/tables you created.