- Here's a great article about the restoration of a type II Curta.

Restoring A Type II Curta - Serial Number 505228 (.pdf) - by KB Model Engineering

It even includes references to the original Curta Factory Drawings. - The Curta Calculator - by Jim Bianchi
- How to Calculate with a Curta - by Nicholas Bodley
- The Amazing CURTA! - by Bruce Flamm
- CURTA 2000 - by George E Heath
- Algorithms for calculating Natural Log and e^x - by Steven Alford
- Calculating Curta square roots - by Daniel F F Ford
- Curta Observations - by Chris Writt
- "Reader's Digest-Crunching Numbers" - by Cliff Stoll
- "Scientific American-The Curious History of the First Pocket Calculator" - by Cliff Stoll
- When was your Curta made? - by Daniel F F Ford
- An algorithm for long divisions - by Silvio Henin
- Curta-NYTimes-110652.pdf - from Jim Chen
- Curta-NYTimes-011058.pdf - from Jim Chen
- Curta-NYTimes-050460.pdf - from Jim Chen
- Curta-NYTimes-010961.pdf - from Jim Chen
- Curta-Rally-Popular-Mechanics-1963-July-65-content.pdf
- Curta-Rally-Popular-Science-1966-January-65-content.pdf

(Click here)

Curta Mechanical Calculator as used in TSD rallying by Jim Bianchi

(as published in rallye magazine, March 1976)

- A Nikon MD4 or similar motor-drive

- A hacksaw (18 tooth blade -Curt says it cuts faster)
- A flat bastard file (medium or coarse)
- 3 feet of duct tape (the handyman's friend)
- Black modeler's paint (optional)
- A hot glue gun
- A screwdriver or pry bar

- Take a 2-inch piece of the duct tape and place it on the top of the calculator, under the crank handle.

This will protect the fine finish from being marred by the subsequent sawing and filing. - Locate a line 4mm from the crank axis and cut off the crank with the hacksaw.

*Curt's Tip #1 - Save time and labour! Just saw 3/4 of the way through and pry up on the crank with the screwdriver -

it'll break right off. You've just saved about 15 saw strokes and 20 seconds of time! - Use the flat bastard file to clean up the cut surface of the crank - remember appearance is important

*Curt's Tip #2 - Try to prevent too many of the metal particles generated from the preceding steps from entering the calculator -

they can cause rough operation and binding of the gears. If your unit does seize - just force the crank to work the chunks through.

Use vice-grips if the crank has already been removed. - Apply a bit of black paint to the exposed metal on the crank (and any plier marks) - it gives a nice finished appearance.
- If you have one of the early calculators with a rounded dome at the crank axis, flatten it with the file.
- Apply a generous gob of hot glue to the crank stub, and quickly press the drive end of the Nikon motor drive into the soft glue.
- Wrap about 4 turns of duct tape around the now joined calculator and motor drive to permanently connect them together.

*Curt's Tip #3 - Position the motor drive so that it does not interfere with the movement of the setting knobs or the counting dials.

Using the Curta calculator to calculate the Natural Logarithm and Exponential functions without using tables.

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Natural Logarithm

Preliminary requirements: memorize three numbers. Ln(2) = 0.69315 (remember as 6-9-3-15) Ln(5) = 1.60944 (remember as 160-944) Bottom of range = 0.77 Step 1. Eliminate tens For example, if you want to find ln(187.2), you would find ln(100*1.872), which is equal to ln(100) + ln(1.872) Step 2. Move into the "range" by eliminating twos or fives. The "range" is from 0.77 to 2*0.77, or from 0.77 to 1.54. In this case, we would say that ln(1.872) = ln(2*0.936) = ln(2) + ln(0.936).

Note that 0.936 is in the range [0.77,1.54]. Step 3. Use formula for part that is in range. Make sure to subtract 1 first! Note that the Taylor series expansion for the natural log is as follows: Ln(1+x) = (x)/1 (x^2)/2 + (x^3)/3 (x^4)/4 + (x^5)/5 … for -1 < x < 1 < 1 Now a way to show successively improving approximations of this series is as follows: (x)/1 (x^2)/(1*2)

(x)/1 (x^2)/2 + (x^3)/(2*2)

(x)/1 (x^2)/2 + (x^3)/3 (x^4)/(3*2)

(x)/1 (x^2)/2 + (x^3)/3 (x^4)/4 + (x^5)/(4*2)

We will only need to go as far as the second approximation. It can be rewritten as: x + (x/2)(x/2)(x 2)

3A: find x. Since we're using 0.936 = 1+x, we have x = -0.064. 3B: square half of x. So to start to do this on the Curta, we will manually enter |x|/2 on the SR. In this case, 0.064 / 2 = 0.032. Square this to get 0.001024. Now enter this in the SR and clear the RR. 3C: multiply by (x 2) Multiply this by (-0.064 2) on the Curta. Since all the additions in 3C and 3D are negative, you can just do them as positives and deal with the negative sign later. 3D: add in x. Then clear the SR and enter x (-0.064 in this case), and add it in once. Again, since all the additions are negative, you can just do them as positives and deal with the negative sign later. Now you have ln(0.936) = -0.066113536. This will be accurate to within + or - 0.002. The true value is ln(0.936) = -0.0661398. Step 4: Add in your twos and fives We have calculated ln(0.936) = -0.06611. Clear the Curta and put this in the SR, and use one negative turn to subtract it. Now add in ln(2) = 0.69315, memorized above. Now we get ln(0.936)+ln(2)=0.67204, which means that ln(0.936*2) = ln(1.872) = 0.67204. Step 5: Add in your tens. Since we're looking for ln(187.2), we need to further add in ln(2) twice and ln(5) twice. Since we already have ln(2) in the SR, two more positive turns, then two positive turns with ln(5)=1.60944 in the SR. Final result: ln(187.2) on the Curta is 5.23222, + or 0.002. Actual ln(187.2) is 5.23218. Error is 0.00004. Final note on error: Most of the error of + or 0.002 is in the ends of the [0.77,1.54] range. If you subtract 0.001 if you are very close to the ends, in the [0.77,0.82] and [1.49,1.54] ranges, your error will decrease to + or 0.001. -----

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Recap of steps: Step 1. Eliminate tens by division Step 2. Move into the "range" [0.77,1.54] by eliminating twos or fives by division. Step 3. Use formula for part that is in range: ln(1+x) ~= x + (x/2)(x/2)(x 2)

3A: find x.

3B: square half of x.

3C: multiply by (x 2)

3D: add in x.

Step 4: Add in your twos and fives Step 5: Add in your tens. ******************* ******************* Exponential Function (e^x) Preliminary requirements: memorize one number e^0.5 = 1.64872 (remember as 16-48-72) (assuming you have already memorized e=2.7182818.) Step 1: separate out wholes and halves from remaining fraction. Exp(1.74) = Exp(1.5) * Exp(0.24) Step 2: use formula for fraction Note that the Taylor series expansion for e^x is e^x = 1 + (x)/1! + (x^2)/2! + (x^3)/3! + (x^4)/4! + (x^5)/5! … A good approximation for e^x over the range [0,0.5] is: e^x ~= 1 + (x)/1 + (x^2)/2 + (x^3)/5. This can be restated as 0.1 * [(10 + 10x) + (x^2) * (5 + 2x) ] 2A: find square of x 0.24^2 = 0.0576. Now clear the Curta and put this in the SR. 2B: multiply by (5 + 2x) Multiply the 0.0576 by 0.24 twice and by 5 once. You should get 0.315648 2C: add in (10 + 10x) Clear the SR, and add in 2.4 once and 10 once. You should get 12.715648. 2D: Divide by 10 (just move the decimal point). You will now have 1.2715648 Step 3: Multiply by whole and half powers of e. Exp(1.74) = Exp(1) * Exp(0.5) * Exp(0.24) = 2.71828 * 1.64872 * 1.27156 = 5.69874 Actual value is 5.69734, error is 0.00140 -----

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Recap of steps: Step 1: separate out wholes and halves from remaining fraction. Step 2: use formula for fraction: e^x ~= 0.1 * [(10 + 10x) + (x^2) * (5 + 2x)] 2A: find square of x

2B: multiply by (5 + 2x)

2C: add in (10 + 10x)

2D: Divide by 10 (just move the decimal point).

Step 3: Multiply by whole and half powers of e.

Rick Furr (rfurr@vcalc.net)

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