Circles and Uncle Albert

I have been attempting to solve a mystery in the diagram of the vesica pisces. What is the origin of the arc between the center point and point K? I want to see the proof that IK has length phi, even though i can see that it does. All help will be appreciated.

To me, talking circles is grand theater. My hypothesis is that the irrational numbers pi and phi have the relationship that two phi equals pi. This does not work in base ten, but then, neither does nature. The difference between the values is something that i call wiggle room. The arc seems to be related to a nautilus shell, if that puts us any closer. I am fairly certain that the original reference must discuss this, but the pdf creator was not interested.

I have also been attempting to reconfigure the definition of time - it doesn't work as a linear function. Once you delete time from the playbook, because using units of time in a definition of time is not allowed, you find that you also have to suspend most mathematics - including calculus which relies extensively on the value d(t). My group theory background has allowed me to derive matrix algebra from chemistry (irreducible representations) and this group has defined sacred geometry as a non-mathematical symmetry based field outside the requirement for math. Beyond that, i guess we can count.

Nature uses sacred geometry extensively. If i am successful, i hope to be able to predict emergent behavior as size and scale increase. The Fibonacci ratio is embedded all over nature - bio-mimicry offers a solution. The problem is that what we know about nature is formed within the context of our thinking and we seem to be too vain to listen to nature rather than superimpose our theories.

Einstein said that imagination is more important than knowledge - it gave him the right to go where ever he wanted without proof. Today, he wouldn't have his thesis read, because he was incapable of jumping through the hoops imposed by the gatekeepers.

Einstein also said that great spirit encounter violent opposition from mediocre minds. Thanks for working on this with me.