[ARTICLE] Structure of Molecular Water and the 3D Pythagoras Theorem (Canadian Journal of Applied Physics Research / 2024)
Creators: name: Teia, Luis
Publisher: name: figshare
Year: 2024
Subjects: classificationCode: 401207
subject: Fundamental and theoretical fluid dynamics
classificationCode: 401299
subject: Fluid mechanics and thermal engineering not elsewhere classified
classificationCode: 401201
subject: Aerodynamics (excl. hypersonic aerodynamics)
classificationCode: 401210
subject: Microfluidics and nanofluidics
classificationCode: 490107
subject: Mathematical methods and special functions
classificationCode: 490109
subject: Theoretical and applied mechanics
classificationCode: 490199
subject: Applied mathematics not elsewhere classified
classificationCode: 490203
subject: Mathematical aspects of classical mechanics, quantum mechanics and quantum information theory
classificationCode: 490299
subject: Mathematical physics not elsewhere classified
classificationCode: 490499
subject: Pure mathematics not elsewhere classified
classificationCode: 499999
subject: Other mathematical sciences not elsewhere classified
classificationCode: 510201
subject: Atomic and molecular physics
classificationCode: 510299
subject: Atomic, molecular and optical physics not elsewhere classified
classificationCode: 510399
subject: Classical physics not elsewhere classified

description: Water ice crystals inherently embed in their shape complex hexagonal structures, emerging mostly due to the O-H bond angle 104.5 degrees being close to the 120 degrees found in hexagons. This article explores the possible integration of water molecules into a recently published mathematical architecture called the Universal Gear model. Already published in a mathematics peer-reviewed journal, the Universal Gear is an orthogonally-intertwined construct of Pythagoras theorem driven planes, that all together provide a perfect balance in terms of the three main equations governing three-dimensional existence: zero net sum of lengths, zero net sum of areas and zero net sum of volumes. Computer-aided Design shows how a group of (simplified and realistic) water molecules successfully integrate into the (regular and irregular) version of the Universal Gear. Interestingly the geometric pattern that emerges from the projected field of water molecules integrated into the Universal Gear is a structure already observed in monuments of ancient civilizations. The ambient conditions, in terms of pressure and temperature, where such a structure could appear is not yet known, requiring further research preferably using computational molecular dynamics.3D CAD available here: https://figshare.com/articles/dataset/_CAD_3D_Model_of_Water_Molecules_x_y_Grouped_as_per_Geometrical_Theorem/26767678?file=48629065Canadian Journal of Applied Physics Research link: https://ccsenet.org/journal/index.php/apr/article/view/0/50127Universal Gear Article link: https://figshare.com/articles/journal_contribution/_ARTICLE_Universal_Gear_and_the_Pythagorean_Theorem_Australian_Mathematics_Education_Journal_2019_/21618003-------------------------------------------------------------------------For more public data, please visit my Figshare profile: https://figshare.com/authors/Luis_Teia/10811244