maths.top

maths.top{a:float, b:float, c:float}

A relation generator for the Triangle Of Power function. Needs at least two arguments. It handles exponents, logarithms and roots in a symmetrical way.

$_{a} {\overset{b}{△}}_{c}$

See Triangle of Power Notation and Logarithms and Triangle of Power (3Blue1Brown on Youtube).

\begin{array}{cclcrcl} _{a} \overset{b}{△}_{} & = & c & ⟷ & a^{b} & = & c \\ _{} \overset{b}{△}_{c} & = & a & ⟷ & \sqrt[b]{c} & = & a \\ _{a} \overset{}{△}_{c} & = & b & ⟷ & \log_{a} c & = & b \end{array}

Examples

power, 2³

import("maths")
print(maths.top(a:=2.0, b:=3.0))

┌──────┐
│ c    │
├──────┤
│ 8.00 │
└──────┘

root, ³√8

import("maths")
print(maths.top(b:=3.0, c:=8.0))

┌──────┐
│ a    │
├──────┤
│ 2.00 │
└──────┘

Note: this relation generator would return both answers for a square root.

log, log₂(8)

import("maths")
print(maths.top(a:=2.0, c:=8.0))

┌──────┐
│ b    │
├──────┤
│ 3.00 │
└──────┘

bulk operation

import("maths")
$P{*, sqw:=maths.top(a:=to_float(WEIGHT), b:=2.0)..c}

sqw PNO PNAME COLOR WEIGHT CITY

144 P1 Nut Red 12 London
144 P5 Cam Blue 12 Paris
196 P4 Screw Red 14 London
289 P2 Bolt Green 17 Paris
289 P3 Screw Blue 17 Rome
361 P6 Cog Red 19 London

sqw	PNO	PNAME	COLOR	WEIGHT	CITY
144	P1	Nut	Red	12	London
144	P5	Cam	Blue	12	Paris
196	P4	Screw	Red	14	London
289	P2	Bolt	Green	17	Paris
289	P3	Screw	Blue	17	Rome
361	P6	Cog	Red	19	London

Note: we need to convert WEIGHT from an int to a float using to_float, and we assume each WEIGHT has only one result, c, otherwise we get an error because ..c would be undefined.

bulk operation, with composition

import("maths")
$P{*, a:=to_float(WEIGHT), b:=2.0}(maths.top)

PNO PNAME COLOR WEIGHT CITY c

P1 Nut Red 12 London 144
P2 Bolt Green 17 Paris 289
P3 Screw Blue 17 Rome 289
P4 Screw Red 14 London 196
P5 Cam Blue 12 Paris 144
P6 Cog Red 19 London 361

PNO	PNAME	COLOR	WEIGHT	CITY	c
P1	Nut	Red	12	London	144
P2	Bolt	Green	17	Paris	289
P3	Screw	Blue	17	Rome	289
P4	Screw	Red	14	London	196
P5	Cam	Blue	12	Paris	144
P6	Cog	Red	19	London	361

Note: we still need to convert WEIGHT to a float but if there were to be multiple results for c (not possible with this example) then we wouldn't error but instead would get extra tuples.

maths.top

a △ b c