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No your domain is the set from which the function transforms from ie F: X->Y the domain is X and the range is Y so in this case domain is the set {A,B,C} and range is {1,2,3}
ok so this is just tons and tons of simple steps but here it goes
first by drawing the pentagon and since parrallel lines connecting the same points are the same line we see that the sets of parrallel lines are
BC DA DC EB ED AC AE BD AB EC
then by using both iscosoles triangle and parrallel line angle theorems (Z patterns) be see
1)DEC=DCE=BCA=CAD=ADE=ECA=CAB let equal x
2)CBD=CDB=BDA=DAE=DBE=BEA let equal y
3) and finally ABE=BEC let equal z
so recap we now have angles (pentagon) which equal
ABC= z+2y BCD=3x CDE=x+2y DEA=x+y+z EAB=2x+y
By looking further at inner triangles
for ADE we see 2y+2x+z=180
and for CDE we see 3x+2y=180 this implies that z=x
Triangle ABC has contains 2 equal angles BAC and BCA which implies iscoscoles and therefore sides
AB=BC which from above also equal DC=DE
this is sufficient enough to say the pentagon is regular
OK so i agree with the poster here on the fact that theorem is completely plausible... for the people remarking on the multiplying of pi by 10^(1000001) this is a counter proof for the corollaries and not the original theorem.
As for the probability rebutle... pi is not considered to be random it is infinite not random just as to see no repetition is all that makes it an irrational the fact that the number is in existence proves it is not random. whether or not naturally pi has shown this chain of digits is up to interpretation... personally iwould say no....
and last but not least i see replies based on the basis that an irrational number cannot contain patterns this is false irrational numbers can contain a pattern just not repetition for example the following is indeed irrational however contains a very easy pattern
0.01020304050607080910111213141516171819202122232425262728293031323334353637383940....
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