Simple and beautiful geometric patterns related to computation and divisibilty

concepts can be observed visually in the Number-Charts with various bases.

A 10-base, 100-Chart is shown in the right. What are the colored numbers?

The 100-Chart, and 10,000-Chart with a series of related questions are discussed

in great detail in the LUCIMATH Units "K-2" and "Number Power-1"

(Chapters 'Pre-computation Number Concepts').

Click on the picture to get the interactive applet which will color for you (blue)

the multiples of any number ( 'div' buttons ) in any NxN chart ('Chart' buttons).

Or enter them (and press 'return') in the corresponding windows. Enter 10 for a

100-Chart, 100 for 10,000-Chart. You can even enter 1,000 for 1,000,000-Chart.

This tool allows one to concentrate on discovering or creating various patterns,

finding their interpretations, making reasonable 'guess&check's.

1. How many multiples of 25 (blue spots) are there?

2. What are their 'coordinate' distances from the left and from the top?

3. What is the slope of the line containing two consecutive spots?

4. What other slopes do you see there?

5. For which multiples do the blue cells form 'continuous' lines?

6. There is only 1 spot for multiples of 51 and higher. What are their left-top 'coordinates'?

Some of the answers are expressed in the "floor function" form which is introduced in MCPT "Perspectives on Algebra", Chapter PATT - Pattern Problems.

Slopes are described in the chapter 'Slopes' of the same Algebra Unit.

7. Color multiples of 5 on a chessboard 8x8- Chart. They fill a regular square grid pattern, formed by traditional 2x1 'knight-moves'. Can you form this chart using the applet?

8. For which charts and what multiples do similar square grid patterns exist?

9. What are the "knight-moves" forming these square-grid patterns?

Think of the same questions 1-9 in general: for multiples of d in NxN-Chart