Have you ever thought to yourself, "Gosh, it sure would be nice to do calculations in base-six [that is, seximal or senary] without having to convert into and out of base six for each problem"? Well, this particular frustration, begone!

This is a slide rule for performing several mathematical operation entirely in base six, as promoted by seximal.net. Several slide-discs provide different rules for different computations (though all have a C scale to match the D scale on the body and to provide a reference direction of 1C).

The body should fit easily inside a (modified) DVD or Blu-ray case for easy transport.

Because the ruler is so small, numbers are not part of the models. Post-processing in the form of coloring the points is my solution, as seen in the project preview images. I used acrylic paint applied with toothpicks, as it was on-hand, the least-significant nonzero digit determining the color: C-CI-A-P' scales, 0::pink, 1::black 2::teal, 3::red, 4::blue, 5::orange (I made a mistake early, so 1.3D and 1.4D have black backfill).

The cursor trades visibility of the underlying rules for durability -- the wide and thick cursor 'arm' occludes a portion of the rules underneath, using its centered edge as the cursor line. If desired, print a mirrored cursor model to cover the opposite side, or modify the model with cutouts to better see the rules beneath.

The models were created with somewhat generous tolerances: +/- 0.25mm in the X or Y axes, +/- 0.15mm in the Z axis. Any printer should be able to produce the pieces such that they will fit together and slide acceptably with little to no removal of material. The models do not lock together, and are not print-in-place. In part as a concession to generous (i.e., accessible) tolerances and in part from lack of experience, these parts do not lock together in any way... in practice, this should not cause problems, as a hand or a desk or a case, plus gravity or clamping pressure, will keep pieces together.

The Rules, Their Names and Functions, and Their Points

all numbers in base six... 100 == [36 base-ten], and [10 base-ten] == 14

• C,D : x
  • clockwise from 1C or 1D:
    • 1, 1.02, 1.04, 1.1, 1.12, 1.14, 1.2, 1.22, 1.24, 1.3, 1.32, 1.34, 1.4, 1.42, 1.44, 1.5, 1.52, 1.54, 2, 2.03, 2.1, 2.13, 2.2, 2.23, 2.3, 2.33, 2.4, 2.43, 2.5, 2.53, 3, 3.03, 3.1, 3.13, 3.2, 3.23, 3.3, 3.33, 3.4, 3.43, 3.5, 3.53, 4, 4.1, 4.2, 4.3, 4.4, 4.5, 5, 5.1, 5.2, 5.3, 5.4, 5.5[, 1]
• CI : 1/x
  • same points as C,D, but in the opposite (counterclockwise) direction.
• A : x^2
  • clockwise from 1C:
    • 1, 1.1, 1.2, 1.3, 1.4, 1.5, 2, 2.1, 2.2, 2.3, 2.4, 2.5, 3, 3.2, 3.4, 4, 4.2, 4.4, 5, 5.2, 5.4, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 30, 32, 34, 40, 42, 44, 50, 52, 54[, 100]
• Pprime (P') : sqrt(1+u^2) NOTE: nonstandard rule and label
  • clockwise from out to in:
    • 0, 0.1, 0.2, 0.23, 0.3, 0.33, 0.4, 0.43, 0.5, 0.53, 1, 1.03, 1.1, 1.13, 1.2, 1.23, 1.3, 1.33, 1.4, 1.43, 1.5, 1.53, 2, 2.1, 2.2, 2.3, 2.4, 2.5, 3, 3.1, 3.2, 3.3, 3.4, 3.5, 4, 4.2, 4.4, 5, 5.2, 5.4, 10
    • Used for calculating hypotenuse:
      • c^2 = a^2+b^2
      • ⇒ c^2 = b^2 * ((a/b)^2 + 1)
      • ⇒ c = b * sqrt(1 + (a/b)^2)
      • ⇒ c/b = sqrt(1 + u^2) [where u = a/b ]
    • In general, try to multiply/divide such that a >= b.
    • Divide a by b in a way that puts the divisor (b) at index-one of rule C [1C] ; quotient on rule C is found on Pprime, the point of which coincides with c/b on rule C; as 1C points at divisor on D, point on Pprime also coincides with the real value of c on rule D. Total of one slide move, and one mandatory and one optional cursor move to compute.
      • 1C→bD; |→aD; |⇒C(u); |→uP'; |⇒C(c/b)⇒D(c)
• LL : e^x, x=[~0.01 .. ~10]
  • clockwise from in to out, each crossing of the 1C reference line begins a new row below :
    • 1.01,
    • 1.011, 1.012, 1.013, 1.014, 1.015, 1.02, 1.021, 1.022, 1.023, 1.024, 1.025, 1.03, 1.031, 1.032, 1.033, 1.034, 1.035, 1.04, 1.042, 1.044, 1.05,
    • 1.052, 1.054, 1.1, 1.11, 1.12, 1.13, 1.14, 1.15, 1.2, 1.21, 1.22, 1.23, 1.24, 1.25, 1.3, 1.31, 1.32, 1.33, 1.34, 1.35, 1.4, 1.42, 1.44, 1.5, 1.52, 1.54, 2, 2.1, 2.2, 2.3, 2.4,
    • 2.5, 3, 3.1, 3.2, 3.3, 3.4, 3.5, 4, 4.2, 4.4, 5, 5.2, 5.4, 5.5, 10, 11, 12, 13, 14, 15, 20, 23, 30, 33, 40, 43, 50, 100, 110, 120, 130, 140, 150, 200, 230, 300, 400, 500, 1000, 1100, 1200, 1300,
    • 2000
  • notice that Euler's number e (e^1, ~2.42) occurs inline with 1C reference line and in the middle of the slide-disc (accounting for C and the LL spiral rules)
• S : sin(u)
  • clockwise from 0.55C (points as degrees [in base six]) :
    • 13.3, 14, 14.3, 15, 15.3, 20, 20.3, 21, 21.3, 22, 22.3, 23, 23.3, 24, 24.3, 25, 25.3, 30, 31, 32, 33, 34, 35, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 55, 100, 103, 110, 113, 120, 123, 130, 133, 140, 143, 150, 153, 200, 210
  • 13.3S == 13.3ST == ~0.55C
• ST : sin(u)
  • clockwise from 0.101C (points as degrees [in base six]) :
    • 1.4, 1.43, 1.5, 1.53, 2, 2.03, 2.1, 2.13, 2.2, 2.23, 2.3, 2.33, 2.4, 2.43, 2.5, 2.53, 3, 3.1, 3.2, 3.3, 3.4, 3.5, 4, 4.1, 4.2, 4.3, 4.4, 4.5, 5, 5.1, 5.2, 5.3, 5.4, 5.5, 10, 10.3, 11, 11.3, 12, 12.3, 13, 13.3
  • sine and tangent are "very similar" for small angles so they share this rule
  • 13.3S == 13.3ST == ~0.55C
• T : tan(u)
  • clockwise from 1C (points as degrees [in base six]) :
    • 13.3, 14, 14.3, 15, 15.3, 20, 21, 22, 23, 24, 25, 30, 31, 32, 33, 34, 35, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 55, 100, 101, 102, 103, 104, 105, 110, 111, 112
• P : sqrt(1 - u^2)
  • finds leg of right triangle from hypotenuse and known leg
  • also converts sine to cosine
  • clockwise from 1C (first point closer to 1.1C) :
    • 0.552, 0.551, 0.55, 0.545, 0.544, 0.543, 0.542, 0.541, 0.54, 0.534, 0.532, 0.53, 0.52, 0.5, 0.43, 0.4, 0.33, 0.3, 0.2, 0.1
    • 0.1 doubles as 0.553