Dr Charlotte Harris @Chararella
Loves maths, a dab hand at physics. harris-charlotte.co.uk Joined February 2011-
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1. An extension of LOIR for 2 digit multiplication is the structure for 3 digit multiplication. 2. The result in baseN is correctly formated, or normalised, to give an answer in base12. 3. Every number is multiplied by every other number as can be seen in this unique structure.
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The answer is directly from the multiplication before formatting. Base15 or other base n are needed to provide a framework for BaseN.
What is [4.3.7] × [11.2.8] in BaseN?
Multiply the numbers given for a resulting answer in base15.
Here is an easy one: [4.3.7] × [11.2.8] in base15
Try multiplying [8.4.11] by [3.2.7] in base12. Does this process hold true for BaseN?
This is an example of how to multiply [16.4.12] × [8.5.2] in base17.
Multiplication of bases is a good skill to have if you like BaseN. Try this one: Multiply [5 . 8] × [3 . 4] in base 15.
How do you find 250÷18 in base12?
How do you find 250÷18 in base12?
Find 200÷16 in base8 using base n division.
Use base n division to find 200÷16 in base8.
180÷5=36 Use long division in base7 to illustrate how you come up with the correct answer.
180÷5=36 demonstrate this process in base7
If you do not want a masterclass in base n division, please leave now! Base n division is difficult but a whole lot of fun!
Challenge: to calculate 24 decimal digits of Pi in 24 terms or less.
I think this works out at an accuracy of 58 decimal digits of Pi.
This is an extremely accurate rapid convergence high-precision accuracy of Pi demonstrated by an equation which uses the power series to "shave off" the error from the 22/7 approximation where it can be seen there is a leaning towards a Hypergeometric series.
Showcasing "22/7" with 21 decimal digits of Pi...
(22/7) - (22/7)^-6 - (22/7)^-7.5 - (22/7)^-9 - (22/7)^-10.5 - (22/7)^-12 -(22/7)^-13.5 = π to 7 decimal places.
My "22/7" equation can be worked out on a calculator to give 7 decimal places of π in only 6 terms = 3.1415926
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