Grad (Gon) to Sextant

The revolutionaries wanted to decimalize everything — length (meter), mass (kilogram), time (decimal hours), and angle. The gradian divided a right angle into exactly 100 parts, making it compatible with the new metric system and decimal arithmetic. A slope of 1% grade corresponds neatly to gradian-based calculations. Decimal time flopped within a year, the Republican Calendar lasted 12 years, but the gradian quietly survived in surveying because it genuinely simplifies land measurement calculations.

They're all the same unit — 1/400 of a circle. "Gradian" is the international English term, "gon" is preferred in German-speaking countries and ISO standards, and "grade" is the original French name. The symbol varies too: grad, gon, or superscript g. This naming mess is partly why the unit never gained traction outside continental Europe — nobody could agree on what to call it.

Primarily in civil engineering and land surveying in France, Germany, Switzerland, and Scandinavia. Total stations (electronic surveying instruments) from Leica and other European manufacturers default to gon. Mining engineers in Germany use gon for underground surveys. French national mapping uses grades for geodetic calculations. If you buy a Leica total station in Europe, you may need to switch it from gon to degrees before using it elsewhere.

Calculator manufacturers include DEG, RAD, and GRAD modes because international standards (particularly IEC 60747) require it, and European civil engineering exams expect students to work in gradians. The mode exists for a real user base — it's just a user base concentrated in specific countries and professions. The most common calculator accident in the world is probably getting wrong trig answers because the calculator was accidentally left in GRAD mode after someone else used it.

Multiply gradians by 0.9 to get degrees, or multiply degrees by 10/9 to get gradians. A right angle is 100 grad = 90°. The conversion factor is 9/10 because 400/360 = 10/9. This means 50 grad = 45°, 200 grad = 180°, and 300 grad = 270°. The relationship is simple enough to do in your head, which is one of the few nice things about having two competing angular systems.

A sextant uses two mirrors to superimpose the image of a celestial body onto the horizon. The navigator looks through the eyepiece and sees the horizon directly through a half-silvered mirror, while a second mirror on a movable arm reflects the Sun or star down into the same field of view. You swing the arm until the star appears to sit exactly on the horizon, then read the angle off the graduated arc. The double-reflection design means the arc only needs to span 60° (one sextant) to measure angles up to 120°.

The name refers to the arc of the instrument, not its measurement range. A sextant's arc is one-sixth of a circle (60°), but thanks to the double-reflection principle — where the angle of reflection doubles the arc angle — it can actually measure angles up to 120°. Similarly, an octant (one-eighth of a circle, 45° arc) measures up to 90°. The naming convention describes the physical shape of the tool, not its capability.

Yes, and navies worldwide still require it. The US Naval Academy reintroduced mandatory celestial navigation in 2015 after a decade-long hiatus, citing concerns about GPS vulnerability to jamming, spoofing, and satellite failure. A skilled celestial navigator with a sextant, an accurate clock, and a nautical almanac can determine position to within about 1–2 nautical miles — good enough to make port safely. Several solo round-the-world sailors carry sextants as backup specifically because they have no electronics to fail.

The sextant itself couldn't solve longitude — that required an accurate clock (John Harrison's marine chronometer, completed in 1761). But the sextant was the other half of the solution. A navigator used it to measure the Sun's altitude at local noon to find the exact time of solar noon at their position. Comparing this to Greenwich time on the chronometer gave the time difference, and since Earth rotates 15° per hour, that time difference directly yielded longitude. Sextant + chronometer = position anywhere on Earth.

Sixty degrees is the interior angle of an equilateral triangle — the simplest regular polygon after the square. Honeycomb cells are hexagons (six 120° angles, each the supplement of 60°) because hexagonal packing is the most efficient way to tile a plane. Carbon atoms in graphene and diamond form 60° and 109.5° angles respectively. The 60° angle appears everywhere in nature because it's the geometric consequence of close-packing equal-sized spheres or circles.