A trigonometric function display clock includes a clock face that has a center aligned with a central axis, axial markings aligned with an x-axis and a y-axis, and a secondary circle having a diameter equal to a radius of the axial markings. A first point on the secondary circle is aligned at the center of the central axis, and the secondary circle is configured to be rotatable about the first point. The secondary circle is configured to overlap and align with at least a portion of the axial markings as the secondary circle rotates about the first point.

A wristwatch (an example of a timepiece) includes a small dial (an example of a dial) and a rotary disk (an example of a rotary member). The small dial includes a sun mark for displaying the state of the sun. The rotary disk covers the small dial and rotates in a 24-hour period. The rotary disk includes the sun state indicator that changes the visibility of the sun mark in accordance with the rotational position of the rotary disk. One of the small dial and the rotary member includes a plurality of numbers (an example of indexes) for indicating time. The other of the small dial and the rotary member includes a time indicator that indicates a number in accordance with the rotational position of the rotary disk. The time indicator and the sun state indicator are disposed relative to each other in a positional relationship such that the visibility of the sun mark by the sun state indicator corresponds to the state of the sun corresponding to the number indicated by the time indicator.

A horological mechanism (110), notably a horological movement or chronograph module, including a counting chain (100) having an epicycloidal train (31, 32, 33, 34) including a first sun wheel (33) fixed to the frame.

An improved minute countdown clock is provided that depicts the 24-hour day in terms of the number of remaining minutes, rather than in the standard 12-hour cycle. The present clock counts down the number of minutes that are left in the day, unlike a standard clock that depicts the amount of time that has passed in two separate cycles. The present invention may come in either analog or digital varieties. The present invention breaks time into smaller increments in order to reprogram individuals' concept and perception of passing time, to facilitate motivation to accomplish more goals, and finally to create a sense of value and ownership of personal time. Furthermore, the constant countdown creates a sense of urgency by helping people recognize that time is valuable and is lost once it passes.

An apparatus may include a display for visually representing solar time and civil time simultaneously. In some embodiments, the apparatus includes a representation of a horizon extending across the display, an icon of the sun corresponding to a solar time by its position relative to the representation of the horizon and to a top portion of the display, the icon of the sun configured to revolve once per solar day about a center portion of the display, and a plurality of hour indications corresponding to civil-time hours of a day, the plurality of hour indications set circumferentially around the display. The angular position of the plurality of hour indications may be rotatable, thereby enabling the civil time of solar noon to appear at the top portion of the display.