Divide a big cube into 49 small cubes

  • Context: MHB 
  • Thread starter Thread starter Albert1
  • Start date Start date
  • Tags Tags
    Cube
Click For Summary
SUMMARY

The discussion focuses on the mathematical procedure to divide a large cube with a side length of 1 into 49 smaller cubes. The method involves initially dividing the large cube into 343 smaller cubes, each with a side length of $\frac{1}{7}$. From these, 336 cubes are then reconfigured to create 42 cubes with a side length of $\frac{2}{7}$. This results in a total of 49 cubes, comprising 42 smaller cubes and 7 remaining cubes of the original size.

PREREQUISITES
  • Understanding of geometric principles related to cube division
  • Familiarity with basic algebraic manipulation
  • Knowledge of the OEIS (Online Encyclopedia of Integer Sequences) for reference
  • Concept of cube volume and dimensions
NEXT STEPS
  • Explore the mathematical properties of cube dissection
  • Research the OEIS sequence A014544 for further insights on cube subdivisions
  • Study advanced geometric transformations and their applications
  • Learn about volumetric calculations in three-dimensional geometry
USEFUL FOR

Mathematicians, educators, students studying geometry, and anyone interested in advanced cube dissection techniques.

Albert1
Messages
1,221
Reaction score
0
Please divide a big cube into 49 small cubes
 
Mathematics news on Phys.org
Albert said:
Please divide a big cube into 49 small cubes

[sp]You can be assumed to follow a procedure of this type. Il the side of big cube is 1, then You first divide it into 343 cubes of side $\frac{1}{7}$. Then You use 336 of them to form 42 cubes of side $\frac{2}{7}$, so that at the end 42+7=49 cubes remain...[/sp]

Kind regards

$\chi$ $\sigma$
 
chisigma said:
[sp]You can be assumed to follow a procedure of this type. Il the side of big cube is 1, then You first divide it into 343 cubes of side $\frac{1}{7}$. Then You use 336 of them to form 42 cubes of side $\frac{2}{7}$, so that at the end 42+7=49 cubes remain...[/sp]

Kind regards

$\chi$ $\sigma$
very good ! here is my solution
if the big cake of side 6
divide the cake into three lays:
the first lay of side 2 (9 cakes)
the second lay of side 1 (36 cakes)
the third lay of side 3 (4 cakes)
9+36+4=49
 

Attachments

  • divide cake.jpg
    divide cake.jpg
    14 KB · Views: 96
Last edited:
See A014544 - OEIS for information about the number of sub-cubes into which a cube can be dissected.
 

Similar threads

MHB Sum of Numbers on Cube Faces to Equal 2004
  • · Replies 1 ·
Replies
1
Views
2K
MHB [ASK] Find the volume of Pyramid in a Cube
  • · Replies 6 ·
Replies
6
Views
3K
MHB Is the Sum of Three Cubes Solved for the Number 33 by a Planetary Supercomputer?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Proof that cube roots of 2 and 3 are irrational
  • · Replies 9 ·
Replies
9
Views
12K
MHB X^6 - y^6 As Difference of Cubes
  • · Replies 4 ·
Replies
4
Views
2K
MHB How to Find the Cube Root of a Number?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Calculating G's Distance from BH on an ABCD.EFGH Cube
  • · Replies 2 ·
Replies
2
Views
1K
MHB Find n such that both n+3 and n^2+3 are perfect cubes
  • · Replies 5 ·
Replies
5
Views
2K
MHB Can Two Points in a Cube Be Less Than √(3)/2 Apart?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Perfect Cube & Square: 5-Digit Number
  • · Replies 2 ·
Replies
2
Views
2K