yah well this is a filed of math i'm not sure what it's called
alright well her we go how do I graph on a flat piece of paper in four dimensions. I can do it on the computer simply but I'm not sure how to do it on a flat piece of paper
When you have two misspelled words of four words in your subject line, it's hard to ignore your carelessness.
Are you sure you're serious about getting help in answering this question?
http://en.wikipedia.org/wiki/Fourth_dimension
I've never seen a fourth dimension until the animation in this article. I doubt you can draw that on paper.
http://dna-view.com/triangle.htm
Graphing in four dimensions can indeed be challenging, especially on a flat piece of paper where we are limited to displaying only two dimensions. However, I can explain the concept behind visualizing four-dimensional objects, known as "hyperspace," and provide you with a technique called projection to represent them on paper.
To graph in four dimensions on paper, we need to project the higher-dimensional object onto a lower-dimensional space. Here's a step-by-step approach to help you understand how projection works:
1. Start with a four-dimensional object: In the case of 4D graphing, we typically work with a 4D shape like a hypercube (also known as a tesseract) or a hypersphere. For the purpose of this explanation, let's consider a hypercube.
2. Visualize the lower-dimensional representation: Begin by visualizing the object in three dimensions. A hypercube has a similar structure to a cube, but with interconnected cubes instead of squares as faces. You can try drawing a regular cube, and then imagine connecting the vertices of the cube to form additional cubes in the interior. This represents the 3D projection of a 4D hypercube.
3. Use shading or color coding: To help convey the concept of dimensionality, you can use shading or color coding to differentiate the additional cubes in the interior from the outer cube.
4. Add depth cues: Since we are representing a 3D projection of a 4D object, adding depth cues can enhance the visual understanding. You can use techniques like varying the opacity of lines/cubes, using perspective drawing, or employing lighter shades for sections closer to the viewer and darker shades for sections farther away.
Keep in mind that while this technique of projection can give you a representation of a higher-dimensional object on paper, it still doesn't provide a true visual understanding of the fourth dimension. Our human perception is limited to three dimensions, so we can only approximate and visualize higher dimensions through these projection techniques.
If you want to explore four-dimensional objects more interactively and intuitively, I recommend using specialized software or virtual reality tools designed to visualize hyperspaces. These tools allow you to manipulate and observe 4D objects with greater ease and accuracy.
I hope this explanation helps you understand how to graph in four dimensions on a flat piece of paper.