Delta numerals
In mathematics, a delta numeral is a numeral expressed in the delta numeral system, which represents differences of the exponents of the adjacent distinct powers of 2 in the binary representation of n concatenated as decimal digits. It was invented by Armands Strazds as a derivation from the system of rational numerals. The preferable data type of the delta numeral is an array, since multi-digit items are possible.[1] The individual item of a delta array is referred to as component.[2] Delta components are natural numbers (1..∞) typically represented using either Hindu–Arabic or rational numerals.[3]
Example[edit]
Encoding[edit]
To convert the binary number 1100100010 (decimal 802) into delta numeral:
- 1100100010 → [1, 100, 1000, 10] = [1, 3, 4, 2]
Decoding[edit]
To convert the delta numeral [1, 3, 4, 2] into binary number:
- [1, 3, 4, 2] → [1, 100, 1000, 10] = 1100100010
Induction[edit]
- The leading Ln, n = 2..∞ emits a unit into the "monolith" (1-run) Im, m = 0, ..., ∞ (Fig. upward arrow):
LnIm → Ln–1Im+1 - The "mass" of the monolith is converted into "energy" (Fig. downward arrow):
→ Ln–1Ym+1
In Fig. monolith of n > 1 is marked by the stretched circle.
See also[edit]
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References[edit]
- ↑ "OEIS sequence A275536". The On-Line Encyclopedia of Integer Sequences. Retrieved 28 February 2017.
- ↑ 2.0 2.1 Strazds, Armands (2017). Suranadira: Der Fluss des Himmels und der Töne [Suranadira: The River of Heaven and Tones] (in German) (1st ed.). urn:nbn:de:101:1-201702133788. Retrieved February 24, 2017.CS1 maint: Unrecognized language (link) Search this book on , pp. 129–132
- ↑ Strazds, Armands (2017). Suranadira: Der Fluss des Himmels und der Töne [Suranadira: The River of Heaven and Tones] (in German) (1st ed.). urn:nbn:de:101:1-201702133788. Retrieved February 24, 2017.CS1 maint: Unrecognized language (link) Search this book on , pp. 132–134
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