Help in calculating the square of a number in sexagesimal notation?

  • Context: Graduate 
  • Thread starter Thread starter moohah
  • Start date Start date
  • Tags Tags
    Notation Square
Click For Summary

Discussion Overview

The discussion centers around calculating the square of a number expressed in sexagesimal notation (base 60), with a specific example provided by the original poster (OP). Participants explore methods for performing this calculation without converting to decimal notation, addressing both theoretical and practical aspects of arithmetic in a non-decimal base.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • The OP asks for a method to calculate the square of a number in sexagesimal notation, specifically the number 37 + 4/60 + 55/60^2.
  • Some participants suggest considering how squaring works in decimal notation and question whether the same principles apply in different bases.
  • A participant presents a formula for squaring a polynomial and suggests substituting values for a, b, and c to apply it to the OP's example.
  • Another participant emphasizes the need to define symbols for base-60 integers and create multiplication and addition tables specific to that base.
  • One participant believes that if arithmetic is performed correctly in base-60, the method proposed by another participant would yield the correct result in sexagesimal notation.
  • There is a suggestion for the OP to practice with simpler examples in octal before tackling the sexagesimal case.
  • A participant expresses confusion about the clarity of the discussion, indicating that it may be difficult for those less familiar with the topic.
  • A later reply supports the method proposed by a participant, indicating some level of agreement with their approach.

Areas of Agreement / Disagreement

Participants express differing views on the clarity and correctness of various methods proposed for squaring numbers in sexagesimal notation. There is no consensus on a single approach, and some participants challenge the clarity of the discussion.

Contextual Notes

Some participants note the importance of performing arithmetic strictly in base-60 to avoid errors that may arise from converting to decimal. There are also references to conventions in representing numbers in sexagesimal notation that may not be universally understood.

Who May Find This Useful

This discussion may be of interest to those studying number systems, particularly non-decimal bases, as well as individuals looking to understand mathematical operations in sexagesimal notation.

moohah
Messages
4
Reaction score
0
How would you go about calculating a number's square entirely in sexagesimal notation (i.e. base 60). For example, how would you calculate the square of 37 + 4/60 + 55/60^2? If you can please show me how to calculate a number's square entirely in sexagesimal notation without using decimals it would be appreciated! Thanks in advance for answers...
 
Mathematics news on Phys.org
Some questions to think about that might lead to an answer to your question ...

How do you go about calculating a number's square in decimal notation?

Why/how does that work?

Why does that not work for a different base? Could you change something to make the process work in a different base?
 
(a +b x+c x^2)^2=a^2+2abx+2acx^2+b^2x^2+2bcx^3+c^2x^4
let
a=37
b=4
c=55
x=1/60
then carry
 
First step would be to define symbols for your 60 integers, then work out multiplication and addition tables in terms of those integers, now multiply.

The trouble with lurflurf's solution is that it is doing the arithmetic in decimal, and the result will be in decimal.
 
As long as lurflurf does his arithmetic in base-60 arithmetic, I believe his method would correctly compute the base-60 square of that number in base-60 notation.

Personally I think the OP should first do some simple ones. How about octal? Won't that work with the number he gave or even a simpler number? Try squaring some simple numbers in just plain-old octal first, then ramp it up.
 
Last edited:
^No that is sexagesimal. We could use a=10 z=35 A=36 X=59 to conform with convention

B.4T=B*1+4*0.1+T*0.01

for one example
a.bc
is perfectly adequate
 
. . . I don't know what none of you guys are doing in this thread to be honest with you. It's ambiguous, unclear, and confusing to someone at the top in class.
 
Hey lurflurf has it right... thank you guys for your help
 

Similar threads

  • · Replies 16 ·
Replies
16
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 15 ·
Replies
15
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
2
Views
2K
  • · Replies 19 ·
Replies
19
Views
4K
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
Replies
2
Views
4K