-ANGULAR REFERENCES-

-as of [23 MARCH 2026]-

.

*3 DIMENSIONS* —>

-THE [STERADIAN]-

.

*2 DIMENSIONS* —>

-THE [RADIAN]-

-THE [DEGREE]-

.

[2π] radians = [360°]

[π] radians = [180°]

[1] radian = [57.2957°]

[1°] = [0.01745] radians

.

π

.

-TO CONVERT “DEGREES” TO “RADIANS”, MULTIPLE THE [DEGREE VALUE] BY [π / 180]-

[π / 180] ≈ 0.01745

.

-TO CONVERT “RADIANS” TO “DEGREES”, MULTIPLE THE [RADIAN VALUE] BY [180 / π]-

[180 / π] ≈ 57.29578

.

*DEGREE SYMBOL* —>

°

*to type “degree symbol” on macOS* —>

-[SHIFT] + [OPTION] + [ 8 ]-

.

(there is no symbol for “radians”)

.

*ANGLES* —>

-10 ANGLES-
(as of [15 MAY 2025])

.

*minimum* —>

0

-HORIZON-

.

-[6°]-

-CIVIL TWILIGHT-

.

-[12°]-

-NAUTICAL TWILIGHT-

.

-[18°]-

-ASTRONOMICAL TWILIGHT-

.

-[0.666]-

(38.157°)

(POSTERBOARD HORIZONTAL ACUTE ANGLE)

.

-[π / 4]-

(~0.7854)

(45°)

.

-[0.905]-

(51.843°)

(POSTERBOARD VERTICAL ACUTE ANGLE)

.

-[π / 2]-

(~1.5708)

(90°)

.

-[3π / 4]-

(~2.3562)

(135°)

.

π

(~3.1416)

(180°)

.

-[5π / 4]-

(~3.92699)

(225°)

.

-[3π / 2]-

(~4.7124)

(270°)

.

-[7π / 4]-

(~5.4978)

(315°)

.

*maximum* —>

(~6.2832)

(360°)

.

.

*👨‍🔬🕵️‍♀️🙇‍♀️*SKETCHES*🙇‍♂️👩‍🔬🕵️‍♂️*

.

.

👈👈👈☜*-FRAMING DIMENSIONS-* ☞ 👉👉👉

.

.

💕💝💖💓🖤💙🖤💙🖤💙🖤❤️💚💛🧡❣️💞💔💘❣️🧡💛💚❤️🖤💜🖤💙🖤💙🖤💗💖💝💘

.

.

*🌈✨ *TABLE OF CONTENTS* ✨🌷*

.

.

🔥🔥🔥🔥🔥🔥*we won the war* 🔥🔥🔥🔥🔥🔥