matthieupeeters / math-teach

math-teach

Notational improvements to math to make it easier to teach.

Notation for root/log/power: 3 2 V = 2 ^ 3

3 V 8 = 8 ^ (1/3) = cubrt(8)

2 V 8 = log(8) / log(2) = log2(8)

The V can be extended by two outward horizontal lines at the top. In a way that they are above the base and the power. Think of an ordinary √ sign. Of course the exponent can be inside the V shape, as with a ∜ symbol. Note the symetry in this notation.

A complementary notation might make negative numbers easier to gasp, or at least to calculate. To indicate complementary numbers a prefix can be used. For negative numbers the prefix used here is: ९ (U+096F, this is the number 9 in Devanagari, and can also be seen as "below zero"). Another possibility is ߉ (U+07C9) but since it is written right-to-left it makes typing numbers harder.

This symbol of course is not used in the same way as a - sign.

0 = 0 or 00 or 000 etc (all positive numbers can have any number of prefixing zeros, as in normal notation) 1 = 1 or 01 or 001 etc -1 = ९ or ९9 or ९99 or ९९9 etc (not that, at least for now, repeating the sign doesn't change its meaning) -2 = ९8 or ९98 or ९998 or ९९8 etc. (possibly a normalized notation is useful) -3 = ९7 etc. (ex. ९7 + 03 = 00) -4 = ९6 etc. (ex. ९6 + 05 = 01) -5 = ९5 (ex. ९5 + 02 = ९7) -6 = ९4 (ex. ९4 + ९8 = ९2, note the carry-over into ९ dissapears) -7 = ९3 (ex. ९3 + ९3 = ९86, note that the lack of a carry-over into ९ makes it a ९8) -8 = ९2 (ex. ९2 - 01 = ९1 = ९2 + ९9) -9 = ९1 (ex. ९1 - ९8 = ९3, note that the borrow from ९ dissapears.) -10 = ९0 (ex. ९90 + 10 = 0) -11 = ९89 -12 = ९88 -13 = ९87 -20 = ९80 -21 = ९79 -25 = ९75 -50 = ९50 -86 = ९14 -98 = ९02 -99 = ९01 -100 = ९00 = ९900 -101 =९899

(defun display-complement (v) (labels ((invert-decimal (v) (map 'string (lambda (v) (code-char (+ (char-code #\0) (- (char-code v)) (char-code #\9)))) v))) (cond ((zerop v) "0") ((> 0 v) (format nil "९~a" (invert-decimal (format nil "a" (- (1+ v)))))) (t (format nil "0a" v)))))

९2491 ९9432 +

९1923 The carry is absorbed by the two ९'s

02491 00432 +

02923 The carry is handled conventionally.

९2491 09432 +

९1923 The carry is absorbed by the one ९.

02491 ९9432 +

01923

decr 0 <-> 9 1 <-> 8 2 <-> 7 3 <-> 6 4 <-> 5

Duodecimal notation, or at least introductions to the concept, might improve learning fractions. A prefix might be used to distinguish with decimal notation.