Understanding the Difference Between Sophism and Pythagorism in Mathematics

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SUMMARY

This discussion centers on the mathematical concepts of sophism and pythagorism, particularly in relation to angle measurement. Participants highlight the confusion surrounding the use of degrees versus radians, specifically noting that circles traditionally contain 360 degrees, while some argue for the use of 2π radians or even a 400-degree system. The conversation emphasizes the importance of clarity in teaching these concepts to avoid further confusion among students, especially regarding the trigonometric ratios encapsulated in the mnemonic "SOHCAHTOA."

PREREQUISITES
  • Understanding of basic trigonometry, including the "SOHCAHTOA" mnemonic.
  • Familiarity with angle measurement systems: degrees and radians.
  • Knowledge of the historical context of mathematical concepts, specifically sophism and pythagorism.
  • Basic mathematical literacy to comprehend the implications of different angle measures.
NEXT STEPS
  • Research the differences between degrees and radians in trigonometry.
  • Explore the historical significance of sophism and pythagorism in mathematics.
  • Learn about the implications of using alternative angle measurement systems, such as the 400-degree system.
  • Study the application of trigonometric ratios in various mathematical problems.
USEFUL FOR

Mathematics educators, students struggling with angle measurements, and anyone interested in the philosophical implications of mathematical concepts.

waitshift
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Homework Statement
If circles contained 1001 degrees instead of 360 how would sohcahtoa and the math of relevant angles change? What would the number of seconds be in a day?
Will we be able to push scientific reform of our educational systems and interest more people in science?
Relevant Equations
Sohcahtoa
I, being a not very accomplished mathematician, cannot understand these maths involved.
I understand that circles simply contain 360 degrees, but how does the math differ if they do not?
 
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waitshift said:
but how does the math differ if they do not?
Should be rather insensitive to that. After all, there's a whole lot of folks who think it's ##2\pi## instead of 360. And I think there's even a few that use 400 😳

[edit] I had to look up sohcahtoa -- fortunately trig stuff is mostly ratios, so insensitive.

Also had to look up sophism (well...) and start to feel a bit suspicious now :rolleyes:

And we already have plenty students who have problems with the radians/degrees setting of their calculator, so let's not add another measure for angles, please :smile:
 

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