Is mn+m-1 of golden ratio?
References
0,1,1,2,3,5,8,13,21,. . . . is of golden ratio. 1.61803
1+1/(1+1/(1+1/ . . . is of golden ratio. 1.61803
m^2-m-1=0 gives 1.61803 and -0.61803.
Points to think of
Slight variants to m^2-m-1 give golden ratios. For example m^2+m-1=0.
Other equations like m^2-2-1/m and their slight variants give golden ratios.
My stance
1.61803 and 0.61803 are important. g and g-1. Consecutive numbers sort.
There are two values to golden ratio. Instead of the quadratic expression m^2+m-1 , I have used mn+m-1..
What I feel like
It is appropriate to claim mn+m-1 is of golden ratio.
Suppose there are two values to m^2+m-1=0.
ReplyDeleteThey can be only m^2+m-1=0 and n^2+n-1=0 and certainly not mn+m-1=0.
Point taken.
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ReplyDeleteLet us dig further . . .
ReplyDelete26 apples cost 5 times the cost of 10 bananas.
ReplyDelete10 bananas plus 5 rupees makes 100 rupees.
Solving equations like these have to be approved by teachers and above us guys.
only 4 percent of guys are interested.
96 percent want to know the difference between mn+m-1 and nm+n-1 approaches.
ReplyDeleteThis is what I feel.
Indians have not made much contributions to mathematics. Stephen Hawking wrote so. And I believe that.
ReplyDeleteSrinivasa Varadhan is exceptional.
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This finishes. Unless someone comments here. Then I shall reply.