Properties
Tallying is often referred to as "base 1", since only one mark – the tally itself – is needed. This is more formally referred to as a unary numeral system. Unlike base 2 or base 10, this is not a positional notation. Since the base 1 exponential function (1x) always equals 1, its inverse does not exist (which would be called the logarithm base 1 if it did exist). There are two ways to write the real number 1 as a recurring decimal: as 1.000..., and as 0.999.... 1 is the first figurate number of every kind, such as triangular number, pentagonal number and centered hexagonal number, to name just a few. In many mathematical and engineering problems, numeric values are typically normalized to fall within the unit interval from 0 to 1, where 1 usually represents the maximum possible value in the range of parameters. Likewise, vectors are often normalized into unit vectors (i.e., vectors of magnitude one), because these often have more desirable properties. Functions, too, are often normalized by the condition that they have integral one, maximum value one, or square integral one, depending on the application. Because of the multiplicative identity, if f(x) is a multiplicative function, then f(1) must be equal to 1. It is also the first and second number in the Fibonacci sequence (0 being the zeroth) and is the first number in many other mathematical sequences. The definition of a field requires that 1 must not be equal to 0. Thus, there are no fields of characteristic 1.
Another classification is according to the degrees of freedom allowed, and distinguished between joints with one, two or three degrees of freedom. A further classification is according to the number and shapes of the articular surfaces: flat, concave and convex surfaces. Types of articular surfaces include trochlear surfaces. Biomechanical classification
Joints can also be classified based on their anatomy or on their biomechanical properties. According to the anatomic classification, joints are subdivided into simple and compound, depending on the number of bones involved, and into complex and combination joints:
Simple joint: two articulation surfaces (e.g. shoulder joint, hip joint)
Compound joint: three or more articulation surfaces (e.g. radiocarpal joint)
Complex joint: two or more articulation surfaces and an articular disc or meniscus (e.g. knee joint)

Anatomical
The joints may be classified anatomically into the following groups:

Joints of hand
Elbow joints
Wrist joints
Axillary joints
Sternoclavicular joints
Vertebral articulations
Temporomandibular joints
Sacroiliac joints
Hip joints
Knee joints
Articulations of footUnmyelinated nerve fibers are abundant in joint capsules and ligaments as well as in the outer part of intraarticular menisci. These nerve fibers are responsible for pain perception when a joint is strained. Clinical significance
Damaging the cartilage of joints (articular cartilage) or the bones and muscles that stabilize the joints can lead to joint dislocations and osteoarthritis. Swimming is a great way to exercise the joints with minimal damage.A joint disorder is termed arthropathy, and when involving inflammation of one or more joints the disorder is called arthritis. Most joint disorders involve arthritis, but joint damage by external physical trauma is typically not termed arthritis.