Ask HN: Can calculus be taught without differentiating or integrating by hand?

1) At hight school level, could always do a concise refresher linking algebra/geometry; algebra/gemetry/imaginary numbers as dual number concept staring with making 2 slide rules out of a 2 similar circular item via using compass (10 equal slices) . (aka identity unit & importance of continuity of units & number base / denominator in fractional notation / continutity)

   Exchange one circle with someone else in class -- can you sill generate same slide rule results 
   as other students?[0][1][3]

   note: square viewed on edge is a line!
   note: circle start/end implied vs. linear scale has explicet stop/end point. 
         Unit circle from trig is "1".
         
   Note: IF get rid of the 'circle arc' at bottom of triangle[2] & put into another "scale", then 1 "unit" is combined 'triangle' & circle arc fragment.  Comput the 1 circle arc unit 'size' using trig less one unit triangle area. 
        Or do appropriate 'fold' to push the circle arc into different dimentional plane. 
        aka you've just defined what lies  above pascal's triangle : https://www.youtube.com/watch?v=q2daqMR3l24

   1d pacman : https://news.ycombinator.com/item?id=38845510
   "15" is wrong : https://www.youtube.com/watch?v=FG0vtPa0UrM

2) Dual numbers and trig quadrants!

   a) What's the value of i? square root of i equal? : https://www.youtube.com/watch?v=2OIiLu5xn-E

      How does the resulting unit look in each of the unit circle quadrants? What would happen if added another line? aka instead of abcd, abcde?

'

   b) Automatic differentiation : https://blog.demofox.org/2014/12/30/dual-numbers-automatic-differentiation/

3) the easy stuff -> calculus delta & epsilon, integrands as triagle corners/log end points/circle end/start & evaluation as where dual numbers meet.

4) Time to inflate the log scale / line above into square (no euler yet!)

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[3] category theory abstract nonsense : https://www.youtube.com/watch?v=igf04k13jZk / https://www.youtube.com/watch?v=DrldYpmwN5s

[2] what is the opposite of a set : https://www.youtube.com/watch?v=SrltwGJAiCM

[1] what happens if you add fractions incorrectly : https://www.youtube.com/watch?v=4d6YrTKmjfE

[0] make your own slide rule : https://www.mathed.page/calculator/super-sci/slide.pdf