9fa44c4b-a514-4928-819e-0a2df6c50ca3 70 6 6 decimal

&[DATE] &[TIME] - &[FILENAME]

j 1 - sqrt :

User imaginary

Install at the top of the work sheet CWD C:\SmathFile CurrentDirectory :

Now, 'j' is reserved, i.e: don't index 'j'

On-fly radian/angle calculator

Angle y 03 π * 0.01 range : n 1 y rows range x n el n : rad n el 1 j y n el * + arg eval : 21 line for x rad ° / augment 31 line :

x 0.05967668696 :

y 0.00681261948 j * - :

x y + arg 0.113667 -

x y + arg ° 6.512624 -

Sanity Angle 1 j 1 * + arg ° 45

Sanity Angle 1 - j 1 * + arg ° 135

Unary angle scanner for QuickPlot

Angle 101 45 + 20 red 1 5 mat 2 1 sys

° 1 :

Sanity: observe rotation 1 - j 1 * - arg ° 135 -

Angle 1012 el ° 45

Angle CWD Angle wfile 1

angle CWD Angle rfile :

The crappy unit in 4 counts:

0. X_Y plot rejects 'Angle' => spool to file. 1. spool to file freaks the data 'Angle'. 2. sensless salvage manipulation 3. On-fly and sanity, unit ° [implict *] OK In the program: must divide by °... crazy !

row(Angle) => last value in col 2
equivalent to rows(Angle), faster Angle row 3 π 0.01 / * : Ceil 943

upangle angle 1 col angle 2 col π 2^* ° 2^/ augment :

upangle

rescue 'angle'

11 j * + arg 0.785398

angle 1012 el π 2^* ° 0.785398163397448

0.785398163397448 ° 45

angle 1012 el π 2^* (° / ° 45

j 1 - sqrt :

User Imaginary

Angle from user imaginary

arg("complexNumber") - Returns the angle from the real axis to the given complex number

x C 1 x - (1 x + (* sqrt 1 x - (1 x + (* sqrt - 21 mat :

C x0 11 - 0.99 range : m 1 x0 rows range C0 m el 1 x0 m el - (1 x0 m el + (* sqrt : for x1 1 - 1 0.99 - range : n 1 x1 rows range C1 n el 1 x1 n el - (1 x1 n el + (* sqrt - : for circle x0 C0 augment x1 C1 augment 21 mat : 51 line :

X 001022 mat :

Y 101222 mat :

Ω 001222 mat :

p C 1 el C 2 el X Y Ω 51 sys :

angle: default [radian] 1 j 2 * + arg 1.107149

angle: user [degree] 1 j 2 * + arg ° 63.434949

1 j 2 * + arg ° 180121 - sqrt * + arg * π /

1 j 2 * + arg ° 63.434949

User Unit System

rotation blue ±x+jy ≡ red ±x-jy ≡ 21 mat

° 1 :

radian2degree conversion 180 π / 1 j 2 * + arg * ° 63.434949

° 180 π / :

1 j 2 * + arg ° * 63.434949

Earth distance

Latitude . . Longitude

Drummondville [QC] Canada

Φ2 45.8833 :

λ2 72.4833 :

Oxford [UK]

Φ1 51.7520 :

λ1 1.2577 :

ΔΦ Φ2 Φ1 - : 5.8687 -

Δλ λ2 λ1 - : 71.2256

Φm Φ2 Φ1 - 2 / : 2.93435 -

R 6371 : Earth radius km ≡

km 1 :

2 π * R * km 40030

D π 180 / R * ΔΦ (2^Φm cos Δλ * (2^+ sqrt * : km 7778

This JavaScript uses the Haversine Formula (shown below) expressed in terms of a two-argument inverse tangent function to calculate the great circle distance between two points on the Earth. This is the method recommended for calculating short distances by Bob Chamberlain (rgc@jpl.nasa.gov) of Caltech and NASA's Jet Propulsion Laboratory as described on the U.S. Census Bureau Web site. Note: this formula does not take into account the non-spheroidal (ellipsoidal) shape of the Earth. It will tend to overestimate trans-polar distances and underestimate trans-equatorial distances. The values used for the radius of the Earth (3961 miles & 6373 km) are optimized for locations around 39 degrees from the equator (roughly the Latitude of Washington, DC, USA).

dlon = lon2 - lon1 dlat = lat2 - lat1 a = (sin(dlat/2))^2 + cos(lat1) * cos(lat2) * (sin(dlon/2))^2 c = 2 * atan2( sqrt(a), sqrt(1-a) ) d = R * c (where R is the radius of the Earth)

a ΔΦ 2 / sin (2^Φ1 cos Φ2 cos * Δλ 2 / sin (2^* + :

c 21 a - sqrt a sqrt mwatan2 * : 2.846053

D R c * : 18132

c 2 a sqrt 1 a - sqrt mwatan2 * : 0.295539

D R c * π * : 5915