Dear Yousef, there is a well known experiment in physics which shows that space is closed by three dimensions.

Math — as the formalism — could not bring news for physics.

Thanks to reply peter but math as ideal world and existance of abstract object do not have any limitation .now adays there are alot of theory in physics which require more dimension .any how there is posiblity for existance of higher dimension in nature which our math can not suport them

Math isn't any object. Math is the formalism. If the formalism goes its own way we are not able to find the isometry. If not on isometry, no formalism!

Space is done by power three. Math can deal with power n. See old math.

What is dimension? This is the question.

Dear Yousef, we can not give "names" for each dimension n>3, because we would need an infinite number of names! ( How to name the cube in the space with 357 dimensions? ) If n>3, it's sufficient to add prefix "hyper", and every mathematician will understand correctly the sense!

The best description is in the case of dimension n=3. We have the cube, having as faces 6 bounded pieces from planes( that is 6 equal squares situated in 6 different planes).

The analogue of cube in dimension n=2 is the square( not the rectangle) having as "faces" 4 equal segments situated on 4 different lines.

The analogue of cube in all other n - dimensional space Rn with n>3 is called hypercube.

The hypercube in 4 dimensions has equal cubes as faces and each such face is situated in a 3 - dimensional space R3.

The hypercube in 5 dimensions has equal hypercubes from R4 as faces.

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No contradiction, all clear!

Analogue regarding the sphere! Sphere in 3 dimensions, circle in 2 dimensions, hypersphere in all dimension n>3 . Here the equations defining all such math objects are extremely obviously similar.

Hypercubes and hyperspheres have hypervolumes !

So, to study efficiently and seriously string theory you need more and more advanced mathematics!

Mathematics has indeed progressed significantly, paralleling advancements in contemporary science. Let’s explore your questions about dimensions and their geometric characteristics:

2D Rectangle:

Components: LinesGeometric Characteristics: Perimeter and Area

3D Cube:

Components: Planes (faces)Geometric Characteristics: Surface Area and Volume

4D Hypercube (Tesseract):

Components: 3D volumes (cubes)Geometric Characteristics: Hyper-surface area and Hyper-volume

When we move to the 4th dimension, the components of a hypercube are 3D cubes. The geometric characteristics extend to hyper-surface area (analogous to surface area in 3D) and hyper-volume (analogous to volume in 3D).

5D and Higher Dimensions:Components: For a 5D hypercube, the components are 4D hypercubes.Geometric Characteristics: These include hyper-surface area and hyper-volume, but in higher dimensions, these terms become more abstract and are often referred to as n-dimensional volume or content.

Mathematics does have tools to study higher dimensions, especially through the fields of topology, algebraic geometry, and theoretical physics. Complex geometric shapes in higher dimensions are studied using advanced mathematical concepts and techniques.

String Theory and other modern physical theories indeed require the study of multiple dimensions beyond the familiar three. These theories often involve 10 or 11 dimensions, where the extra dimensions are compactified or curled up in such a way that they are not observable at macroscopic scales.

This answer was generated by AI.

appelé espace vectoriel de quatre dimensions ou plus, un espace vectoriel de dimensions supérieures en mathématiques. Nous devons se pencher sur ces espaces et examinons leur comportement, leurs opérations et leurs interrelations. En comprenant ces dimensions étendues, nous sommes en mesure d'explorer des concepts mathématiques complexes et de les appliquer à divers domaines scientifiques et technologiques.