Fiboquadratic Sequences and Extensions of the Cassini Identity Raised From the Study of Rithmomachia
Tom\'as Guardia, Douglas Jim\'enez
TL;DR
This paper introduces fiboquadratic sequences as an infinite extension related to Rithmomachia, demonstrating their connection to Cassini's Identity and providing new mathematical insights.
Contribution
The paper defines fiboquadratic sequences and shows how they extend Rithmomachia's structure and Cassini's Identity.
Findings
Fiboquadratic sequences are infinite extensions of Rithmomachia.
These sequences extend Cassini's Identity.
New mathematical properties of fiboquadratic sequences are established.
Abstract
In this paper, we introduce fiboquadratic sequences as an extension to infinity of the board of Rithmomachia and we prove that this extension gives raise to fiboquadratic sequences which we define here. Also, fiboquadratic sequences provide extensions of Cassini's Identity.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Mathematics and Applications · Advanced Mathematical Theories and Applications