To create an extensible platform, we’ll start with the most simple mathematics and geometry and slowly build up to the most complex.

On Unifying Theories of Mathematics

An index for an in depth study of each of the 202 notations: A work-in-progress
Prime number notations are in red; those highlighted (yellow) have some data.

The ∞∞∞∞∞.
∞200201202∞∞∞∞∞∞∞∞
∞190191192193194195196 197198199 ∞
∞180181182183184185186187188189∞
∞170171172173174175176177178179∞
∞160161162163164165166167168169∞
∞150151152153154155156157158159∞
∞140141142143144145146147148149∞
∞130131132133134135136137138139 ∞
∞120121122123124125126127128129∞
∞110111112113114115116117118119∞
∞100101102103104105106107108109∞
∞90919293949596979899∞
∞80818283848586878889∞
∞70717273747576777879∞
∞60616263646566676869∞
∞50515253545556575859∞
∞40414243444546474849∞
∞30313233343536373839 ∞
∞20212223242526272829∞
∞10111213141516171819∞
∞..0....1....2....3....4....5....6....7....8....9.. ∞
∞∞∞∞∞∞∞∞∞∞∞∞

Highly-integrated, Mathematical UniverseView

Infinity:  The symbol for infinity surrounds every number. Naturally page layout is two dimensional. Imagine if you will that it is three dimensional and that infinity touches every cell both above and below, and then on every corner so the three faces of infinity — continuity, symmetry and harmony — have a direct finite relation.

Primes: Priority will be given to those notations that are prime numbers. Each prime number is bold red.  #2 is the first prime.  0, the transformation number, is reserved for the natural units.  It is postulated that each prime represents a new mathematical system yet each still builds successively on the all the other notations preceding it given that it is all a base-2 progression. So, although unique, it is an intimate part of the whole.

Below thresholds of measurement (18 prime numbers): 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59 and 61. [All the disciplines mentioned within functional analysis are candidates for these primes.]

From 1-to-202 there are 45 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 197, and 199.

From 0-to-67 there are 19 primes.

1 and 9:   2, 3, 5 and 7
10 to 19:  11, 13, 17 and 19
20 to 29:  23 and 29
30 to 39: 31 and 37
40 to 49: 41, 43, and 47
50 to 59: 53 and 59
60 to 69: 61 and 67

From 68 to 134 there are 13 primes.

70 to 79:  71, 73 and 79
80 to 89: 83 and 89
90 to 99:  97
100 to 109:   101, 103, 107, 109
110 to 119:  113
120 to 129:  127
130 to 139:  131, 137, 139

From 134 to 202 there are 13 primes.
140 to 149:  149
150 to 159: 151 and 157
160 to 169: 163 and 167
170 to 179:  173 and 179
180 to 189: 181
190 to 199: 191, 197 and 199
200, 201, 202: None

The postulation is that each of these 45 prime numbers supports a new mathematical/geometric system that initiates even more diversity and complexity.

FYI Primes: 200 to 1000 are 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 983 991 997 1009

Please note: There are HTML coding issues that need to be resolved. Each of the prime cells are bold red.

color

Animation showing how the sine function (in red) y = sin ⁡ ( θ ) {\displaystyle y=\sin(\theta )}

y=\sin(\theta )

Graphed from the y-coordinate (red dot) of a point on the unit circle (in green) at an angle of θ. https://en.wikipedia.org/wiki/Sine

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