This discussion centers on the challenge of visualizing and charting the fourth dimension within a three-dimensional Cartesian plane. Participants clarify that a plane is inherently two-dimensional and that while mathematical objects can exist in higher dimensions, they cannot be visualized in the same way as three-dimensional objects. The conversation highlights the importance of understanding foundational mathematical concepts such as the Quadratic Formula and the limitations of visualization in mathematics. Ultimately, the discussion emphasizes the need for a solid grasp of Algebra and Calculus to engage with theoretical mathematics effectively.
PREREQUISITESMathematicians, students of mathematics, educators, and anyone interested in the theoretical aspects of higher dimensions and their applications in various fields.
Your question is unclear. A plane is inherently two-dimensional. A plane can be embedded in three-dimensional space, though.shawnr said:Do you just cube a variable? How does it work?
Has this been figured out yet? Any thoughts if it hasn't? Any applications if it has?
The Cartesian plane is two-dimensional, so there are only two axes, typically x and y. There are not three axes.shawnr said:Like z-y-x axis Cartesian plane.
? I don't know what you're saying here.shawnr said:I'm only slightly educated.
you can map the 0th, 1st, 2nd, and 3rd on number line (or first dimension plane[excuse the term]).
Or here, either.shawnr said:You can see each dimension's interpretation on other dimensions. The only difference being variables used. How does the fourth look on the third?
The Quadratic Formula is used to find the two solutions of a general quadratic equation -- ax2 + bx + c = 0. Maybe you're thinking of the area of a square, A = x2, or the volume of a cube, V = x3.shawnr said:If the quadratic formula represents the actions or operations of third
We live in a three-dimensional world. Most of us cannot visualize a space with more than three dimensions. In mathematics there are objects with more than three dimensions, but you can't visualize the space that they belong to.shawnr said:, would cubing a variable on the third dimension be enough to suffice fourth dimensional operations
shawnr said:Somebody else. You're too applicable. This is a pure mathematics question.
Bringing up a synonym doesn't demonstrate you understand the concepts inherent in it.shawnr said:What is Theoretical Mathematics? Now can you answer mine.
I don't know how to break down the word theoretical any farther without sounding pretentious. I will do my best: Theoretical anything is the point at which you develop frameworks for knowledge. If knowledge would be applicable then the frameworks for theoretical would be considered wisdom. So math wisdom is what we are dealing with. More precisely, while applicable allows use of gained wisdom to apply towards real-world problems, theoretical is the search for new knowledge in the hopes of breaking ground for the applicable world. The Greeks were extremely theoretical until Alexandria became the capitol of thought in the classic world.pwsnafu said:Bringing up a synonym doesn't demonstrate you understand the concepts inherent in it.
Look, you've claimed Mark is "too applicable" (sic), and yet he's given you pure math answers. Secondly, visualization of mathematics is not mathematics. Thirdly, you're post makes no sense.