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How to make it in a A4 sheet paper What should be the circle diameter and A4 sheet border length which to be left and diagonal length
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The pattern is a 6 columns × 9 rows grid. Now let me calculate all the measurements precisely.
A4 Paper Scale Wave Pattern - Complete Measurements
A4 Sheet Dimensions
- Width: 210 mm
- Height: 297 mm
Step 1 - Choose Your Border (Margin)
A clean border of 15 mm on all sides works well for A4.
- Usable width: 210 - 15 - 15 = 180 mm
- Usable height: 297 - 15 - 15 = 267 mm
Step 2 - Circle Diameter
The pattern has 6 columns across and 9 rows down. In this wave/scale pattern, each circle is folded into a semicircle, and the circles overlap by half - so:
-
Horizontal fit: 6 circles across 180 mm
- Circle diameter = 180 ÷ 6 = 30 mm
-
Vertical check: Each row steps down by one radius (15 mm), so total height used:
- First row center at 15 mm, then 8 more steps of 15 mm = 15 + (8 × 15) + 15 = 135 mm (fits easily in 267 mm)
With 30 mm circles and 9 rows, the pattern fills the sheet nicely with breathing room at top and bottom.
Step 3 - All Key Measurements Summary
| Measurement | Value |
|---|---|
| A4 sheet size | 210 × 297 mm |
| Border/margin (all sides) | 15 mm |
| Usable area | 180 × 267 mm |
| Circle diameter | 30 mm |
| Circle radius | 15 mm |
| Number of columns | 6 |
| Number of rows | 9 |
| Total circles needed | 54 circles |
| Grid spacing (horizontal) | 30 mm (center to center) |
| Grid spacing (vertical) | 15 mm (center to center, half overlap) |
Step 4 - Diagonal Length of One Circle
The diagonal (diameter) of each 30 mm circle is simply:
- Diagonal = 30 mm (it's the diameter itself for a circle)
If you mean the diagonal of the square grid cell (30 mm × 30 mm):
- Diagonal = √(30² + 30²) = √1800 = 42.4 mm
If you mean the diagonal of the usable area (180 × 267 mm):
- Diagonal = √(180² + 267²) = √(32400 + 71289) = √103689 = ≈ 322 mm
Step 5 - How to Make It
- Cut 54 circles of 30 mm diameter from colored paper (navy, red, white - 18 each)
- Fold each circle in half to make a semicircle
- On your base A4 sheet, mark a grid starting 15 mm from each edge, with dots every 30 mm across and every 15 mm down
- Glue the flat edge of each folded semicircle to the base sheet, aligning to your grid dots
- Alternate rows - odd rows start flush left, even rows offset by 15 mm to create the interlocking wave
The 3D curve forms naturally when the semicircle's flat folded edge is glued flat and the curved part bows upward!
Say the measurements in cm
A4 Paper Scale Wave Pattern - Measurements in CM
A4 Sheet Size
- Width: 21 cm
- Height: 29.7 cm
Border / Margin (all sides)
-
1.5 cm on all four sides
-
Usable width: 21 - 1.5 - 1.5 = 18 cm
-
Usable height: 29.7 - 1.5 - 1.5 = 26.7 cm
Circle Measurements
| Measurement | Value |
|---|---|
| Circle diameter | 3 cm |
| Circle radius | 1.5 cm |
| Diagonal of one grid cell (3 cm × 3 cm) | ≈ 4.24 cm |
Grid Layout
| Detail | Value |
|---|---|
| Columns across | 6 |
| Rows down | 9 |
| Total circles needed | 54 |
| Horizontal spacing (center to center) | 3 cm |
| Vertical spacing (center to center) | 1.5 cm |
Diagonal Lengths
| What | Diagonal |
|---|---|
| One circle | 3 cm (= diameter) |
| One grid cell (3×3 cm square) | 4.24 cm |
| Full usable area (18 × 26.7 cm) | ≈ 32.2 cm |
Quick Reference Card
- Start your first grid dot 1.5 cm from every edge
- Each circle = 3 cm wide
- Place centers 3 cm apart horizontally, 1.5 cm apart vertically
- Cut 18 navy + 18 red + 18 white circles = 54 total
- Fold each in half, glue the flat edge to the base sheet, and the curve pops up naturally!
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