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Which mathematical concepts were the result of the work of René Descartes? Check all that apply.

theory of an Earth-centered universe
formula for the slope of a line
Pythagorean theorem for a right triangle
problem solving by solving simpler parts first
Cartesian plane for graphing
trusting previous teachers for knowledge

11 answers

The mathematical concepts that were the result of the work of René Descartes include:

  • Formula for the slope of a line
  • Cartesian plane for graphing

The other options listed are not credited to Descartes:

  • Theory of an Earth-centered universe: This relates more to astronomy and figures like Ptolemy.
  • Pythagorean theorem for a right triangle: This theorem was known long before Descartes, dating back to ancient Greece.
  • Problem solving by solving simpler parts first: This is more of a general strategy in mathematics and not specifically attributed to Descartes.
  • Trusting previous teachers for knowledge: This is a general educational principle and not a mathematical concept introduced by Descartes.

So, the correct checkboxes are for the formula for the slope of a line and the Cartesian plane for graphing.

nope something aint right either one more answer or one of those TWO are incorrect

Let's reevaluate the options related to René Descartes:

  1. Theory of an Earth-centered universe: Not attributed to Descartes; relates to Ptolemaic astronomy.

  2. Formula for the slope of a line: This can be traced back to coordinate geometry, which Descartes helped develop, making this correct.

  3. Pythagorean theorem for a right triangle: This is an ancient theorem attributed to Pythagoras, not Descartes.

  4. Problem solving by solving simpler parts first: This is a general problem-solving strategy and not specifically attributed to Descartes.

  5. Cartesian plane for graphing: This is directly linked to Descartes, who developed the concept of the Cartesian coordinate system.

  6. Trusting previous teachers for knowledge: This is a general principle of education and not a mathematical concept from Descartes.

The two correct concepts specifically attributed to René Descartes are:

  • Formula for the slope of a line
  • Cartesian plane for graphing

So, my previous conclusion stands correct regarding the notable contributions. If you are considering a broader definition of "mathematical concepts" that includes systematic problem-solving approaches, then you might add that; otherwise, the two specific contributions related to Descartes are indeed the first and fifth options. If there is another answer you had in mind or if there is specific additional context, please let me know!

sieriously choose one more or change on of those becuase it dont count

I apologize for the confusion earlier. Let's clarify the contributions of René Descartes again:

The correct statements related to Descartes' contributions are:

  1. Formula for the slope of a line: Descartes' work in coordinate geometry did lay the foundation for understanding the slope of a line in mathematical terms.

  2. Cartesian plane for graphing: Descartes introduced the Cartesian coordinate system, which is essential for graphing.

After reviewing the options again, I realize that problem solving by solving simpler parts first can also be considered a concept that aligns with methods in mathematics and is broadly employed in problem-solving strategies, potentially influenced by Descartes' methodical approach.

Thus, including that concept, the correct checks would be:

  • Formula for the slope of a line
  • Cartesian plane for graphing
  • Problem solving by solving simpler parts first

So, if we include problem solving by solving simpler parts first, that would be the additional answer to choose. Thank you for your patience!

GOOD!!

Which statement describes the life of René Descartes?

He studied only mathematics his entire life.
He always loved mathematics, but started his career studying law and joining the army.
He devoted his life to the study of what was already known to be true.
He is known as the father of mathematics and the father of psychology.

The statement that best describes the life of René Descartes is:

He always loved mathematics, but started his career studying law and joining the army.

René Descartes initially pursued a legal education and earned a law degree before transitioning into a career that included military service and later focusing on mathematics, philosophy, and science. The other options do not accurately capture the essence of his life and contributions.

What was the purpose of the coordinate graphing system described by Descartes in his book Discourse on Method?

to use algebraic methods to solve geometric problems
to prove the universe was Sun-centered
to represent equations for the queen of Sweden
to prove his own existence

The purpose of the coordinate graphing system described by Descartes in his book "Discourse on Method" was:

to use algebraic methods to solve geometric problems.

Descartes developed the Cartesian coordinate system to bridge algebra and geometry, allowing for the representation of geometric shapes and the solution of geometric problems using algebraic equations. This innovative approach laid the foundation for analytic geometry. The other options do not reflect the primary purpose of his work in this context.

Which procedures are examples of Descartes’s rules for scientific reasoning? Check all that apply.

keeping a detailed record of the procedure and results of a scientific experiment
conducting an experiment to confirm the effects of gravity on Earth
accepting all of Descartes’s theories as truth
answering a math problem using mental mathematics
solving an expression in steps using the order of operations

The procedures that align with Descartes's rules for scientific reasoning include:

  • Keeping a detailed record of the procedure and results of a scientific experiment: This reflects the importance of systematic observation and documentation in the scientific method, which Descartes emphasized.

  • Conducting an experiment to confirm the effects of gravity on Earth: This embodies the principle of experimentation and testing hypotheses, which is central to Descartes's approach to science.

The following options do not align with Descartes's rules for scientific reasoning:

  • Accepting all of Descartes’s theories as truth: Descartes advocated for skepticism and critical thinking, so accepting any theory without question does not align with his principles.

  • Answering a math problem using mental mathematics: While mathematics is important in Descartes's work, this does not directly relate to his scientific reasoning rules.

  • Solving an expression in steps using the order of operations: This is more of a standard mathematical approach than a specific principle of scientific reasoning Descartes promoted.

Therefore, the two applicable options are:

  • Keeping a detailed record of the procedure and results of a scientific experiment.
  • Conducting an experiment to confirm the effects of gravity on Earth.