Solution to Lorenzo's Clock Angle Problem

clock-angle.lisp

(defun h->m (h m)
  (* 5 (+ (mod h 12) 
          (/ m 60))))
  
(defun clock° (h m)
  (let ((° (abs (* 6 (- m (h->m h m))))))
    (min ° (- 360 °))))
  
(write (clock° 11 27))

clock-angle.rkt

#lang racket

(define (hour-position hour minute)
  ; if hour is 12, set to 0, otherwise leave unchanged
  (+ (* 5 (modulo hour 12))
     ; number (in minutes) ahead of hour the hour hand should be
     (* 5 (/ minute 60))))

(define-syntax-rule (time-angle time)
  ; convert 2:20 to the string "2:20". This is impossible in other languages
  (let ((time (symbol->string 'time)))

    (let* ((clock-hands (string-split time ":"))
           (hour (string->number (first clock-hands)))
           (minute (string->number (second clock-hands))))

      (string-append (number->string
      
                      ; convert from 60 minute clock to 360° circle (60 * 6 = 360)
                      (abs  (- (* 6 (hour-position hour minute))
                               (* 6 minute))))
                      
                      ; append degree symbol
                      "°"))))

(display (time-angle 2:20)) ; displays 50°

clockAngle.ex

defmodule ClockAngle do
  def pos(hour, minute) do
    5 * (rem(hour, 12) + minute / 60)
  end
  def angle(hour, minute, second) do
    hour_pos = pos(hour, minute)
    angle = abs(6 * (second - hour_pos))
    inner_angle = min(angle, 360 - angle)

    inner_angle
  end
end

IO.puts ClockAngle.angle(2, 20, 20)

clockAngle.js

let hourPos = (h, m) =>
    5*((h % 12) + (m / 60))

let clockAngle = (h, m) => {
    let angle = Math.abs(6*(m-hourPos(h, m)))
    
    return Math.min(angle, 360 - angle)
}

racket_angle.py

def hourPos(hour, minute):
  return 5 * ((hour % 12) + (minute / 60))
          
def clockAngle(hour, minute, sec):
  angle = abs(sec - hourPos(hour, minute))
  return 6 * min(angle, 360 - angle)


         # h  m   s  
clockAngle(3, 15, 15)

In honor of Lorenzo (an MIT grad) I chose to solve this in Scheme (a language invented at MIT).

You rock, Lorenzo!

The Scheme definitely looks messier, but consider also that I used a macro so you can say (time-angle 7:30), which in Python is outright impossible. Also, I used lots of dumb tricks like (apply - ...) instead of just subtracting the values.

You, dear reader, may not notice because I'm about to beautify it.