Gyrogroups
From mobius to gyrogroups
Groupoids, loops, groups, and gyrogroups
Mobius gyrogroups: from the disc to the ball
First gyrogroup theorems
The two basic equations of gyrogroups
The basic cancellation laws of gyrogroups
Commuting automorphisms with gyroautomorphisms
The gyrosemidirect product
Basic gyration properties
An advanced gyrogroup equation
Exercises
Gyrocommutative gyrogroups
Gyrocommutative gyrogroups
Mobius gyrogroups
Einstein gyrogroups
Gyrogroup isomorphism
Exercises
Gyrovector spaces
Definition and first gyrovector space theorems
Gyrolines
Gyromidpoints
Analogies between gyromidpoints and midpoints
Gyrogeodesics
Mobius gyrovector spaces
Mobius gyrolines
Einstein gyrovector spaces
Einstein gyrolines
Einstein gyromidpoints and gyrotriangle gyrocentroids
Mobius gyrotriangle gyromedians and gyrocentroids
The gyroparallelogram
Points, vectors, and gyrovectors
The gyroparallelogram addition law of gyrovectors
Gyrovector gyrotranslation
Gyrovector gyrotranslation composition
Gyrovector gyrotranslation and the gyroparallelogram law
The mobius gyrotriangle gyroangles
Exercises
Gyrotrigonometry
The gyroangle
The gyrotriangle
The gyrotriangle addition law
Cogyrolines, cogyrotriangles, and cogyroangles
The law of gyrocosines
The SSS to AAA conversion law
Inequalities for gyrotriangles
The AAA to SSS conversion law
The law of gyrosines
The ASA to SAS conversion law
The gyrotriangle defect
The right gyrotriangle
Gyrotrigonometry
Gyrodistance between a point and a gyroline
The gyrotriangle gyroaltitude
The gyrotriangle gyroarea
Gyrotriangle similarity
The gyroangle bisector theorem
The hyperbolic Steiner-Lehmus theorem
The Urquhart theorem
The hyperbolic Urquhart theorem
The gyroparallelogram gyroangles
Relativistic mechanical interpretation
Gyro-analogies that may reveal the origin of dark matter
Newtonian systems of particles
Einsteinian systems of particles
The relativistic invariant mass paradox
Exercises.