Tuesday, January 6, 2026

Two golden ratio expressions

You may recollect that I had developed two golden ratio expressions giving 1.61803 by using expressions similar to the two expressions below.

I have modified the earlier expressions and am now presenting expressions for 0.61803.


Hope you like the expressions.  These are from consecutive numbers. 

Have a nice day !!


And all the four related Golden Ratio expressions






Sunday, January 4, 2026

A pi by 4 formula

I was wondering about five consecutive toes in feet and four consecutive fingers and thumb in hands. 

I used my consecutive number expression mn(n+1). I added 1 for the thumb. Put m equal to 4.

I used the Internet mathematics great Wolfram Alpha.  And got the following result. This is a new result from me on pi.



You may recall Madhava of Sangamagrama gave us pi by 4. Ramanujan gave us 1 by pi apart from other pi results.  Wallis gave us pi by 2 from his product formula.

The above is a product formula and gives us pi by 4. This is the first time I got pi by 4. I got mainly pi by 3 into root 3 in infinite series form.

This tells us importance of 4 and also addition of 1 to it.

Have a nice day !!