Time · Triangle · Centroid

The Dial Triangle

A second take on the time-fix idea, reduced to its cleanest geometry. The angular positions of the hour, minute, and second hands are projected to three points on the rim of the dial — here the south-pole edge of the flat-earth (Gleason) map. Those three points determine one triangle; its centroid — the balance point, the average of the three vertices — is taken as the reference location and lit up on the map. The dial is the Gleason map: the North Pole sits at the centre, so north is not a fixed edge direction — from any point it runs inward toward the centre. The rim is the south-pole edge, and the prime meridian (0°) rises to 12 o'clock with longitude increasing clockwise around it.

time 3 rim points 1 triangle 1 centroid 1 location

Study tool only. A geometric exploration — at certain times (e.g. 12:00:00, when all three hands coincide) the triangle degenerates to a point of zero area; the centroid still resolves to a location, which the readout flags.

The Dial

02:20:13
02
20
13
Speed

Set a time, then start the clock — or sync to your real local time. Either way it ticks forward in real time until you pause.

Centroid

Reference location
triangle area —
Trace style
Color

A second looping line: the instantaneous centre of the circle the trace is bending through at each moment.

Legend

Hour hand Minute hand Second hand Centroid Equator