![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgd5xTkm79trJ5JVeMXQ8vdFyNQnTWtWX2mMPNMlCJyxq51ZQhhaj58j09y89x52xvhfuWbN33gvsKp78J29Tb65Rvkc8fQfCOdHljMj3gw87COlZAdXcVkRih2fbmnmfPsxPmfXBMjb8dx/s400/button.jpg)
1. Start with a circle. Draw lightly if using a pencil, because the circle will be erased later. Make certain the center point is marked.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuj3CxJg_FakquoW5QXl2saE_CFw4ShloeJajLTr9vzY35mikf2B46_w_S2XtPg594PXyKfSr5AlQ_Gq0qqLqYWygWYQ1lkTvRqftK4KWH9lWTPSjYPBMXCVGNq1jcf0xbKTWq0reqfx_w/s400/1.jpg)
2. Using the same diameter, draw circles around the original one, using the intersections as the center points. Each outer circle intersects the center of the original circle.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj0BgGvFXiOW4kgIKCn3r7J3yYAPdteuQT1YmtatSF0eRkcpw3x6C_wKPj1kfxpOtGDg-KtwWFwRkCWxhCaKaw6w675vWVywduMg8WmxtHmFfdR-_Z8QGbndoJI43qlgrNbKPAy4KiT9zTw/s400/2.jpg)
3. Continue until six circles are drawn around the original.
There are a couple of interesting asides:
Six circles, with a constant diameter, fit perfectly, overlapping at the center points, around a center circle with that same diameter.
Also, six circles of the same diameter, fit perfectly around a center circle with that diameter.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh07aXv2a-f_eIfg7YDXUPMfOlrnMe84LY9Hx2MXEwJVM3vQ0Djzvqxj1IhB0Mal4eE4K49gWlrJW3cjBFArauRKYSPuydEmYzYxihzpro7MF5eXN_4CHJV2LICjA2CcDXNXCZugPpexhoR/s400/4.jpg)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKrV5Ur0C353QkD5Ky-ylYnd687mJMMFrhRhL_dyyzzwld9v1QNMdCqExJFnlFh_-HjyjTL0L_E3dbGuT9ubZus_o1ur7gWGHNTGcFVgbQ7AlO6bJ8dRoC8XGI8DMXyXBSlFC4ehUjNhfd/s400/quarters.jpg)
4. Draw sets of parallel lines through the intersection points. Again, if using a pencil, draw lightly because the lines will have to be erased.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjwXfKPhQ_JqaY9fi8eJsxaWiygn2oz1LyhmfN0t6wplW0vgF7Wa2DIQGYiBSmRLTQbshltoZsFMvwhmMnK7HZ74aAnHB5_bBNXxQ9kBCv2sJA49Pn_zbzgQ-Zhb-gOxW_uG_vIishM22j7/s400/7.jpg)
5. Continue, drawing the parallel lines in the 3 possible directions.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiBwN-nJjTLgmdvHRLQ1la_P6aaa2qkMw1TniwS2QrcgMhikn58pmR5-ezsGPIdr3rytGGnnVSDR9p_fe4NjgOhDIpSWYV4zegV62XDdPgCFx2mdKTyWBY4Ags9fw5bELgQ2c6ouYCpBbfM/s400/9.jpg)
6. Erase the original circle design. Continue drawing parallel lines in the three different possible directions. Use the intersection points as guides.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhcjc4OQIU1GF1g0M7fYQZXaLifCKXzbxN3w9NrxzdWuVh5EQdTMt0BU0fUVopB2t4z3AZl46-PBzo-YWJEsogzS51ury2C5MLIZdW2vISJoCFiUU9DR1fEmZkvWnHf28XqM_brxpD8aZm2/s400/11.jpg)
7. More of the same.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-v4RAyz2eXMHL_Bkw4s_mWqQMfza8qsAVze6Dm_Fl54gLQ383QCTc4tEQkSqk4_0XNXTexESFbuO2hdiM3eMsxo2zh_ZyL5ix7GxXbQFsD8Rjl7Oe-sibsw5toI6yyVasImdTA16ovhlV/s400/12.jpg)
8. For my design, I continued until I could draw a hexagon, whose sides were the width of 6 rhombuses.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj07QE9rmPJdgr_YHnaw4teMFvftOElyx32p1WpEBMRBT_7rRVRQu_zFGQtsZ-pWhM7c4WhrxSbJbH58hIWIUWxoUMRPj7VgKCRRM_vo9uknPQLDtcnfD2521cSLydA7dTiQUFMyXBCM2a0/s400/13.jpg)
9. Using the lines, starting from the center, draw a pattern of stars and hexagons. I chose to put a star at the center, but it could easily have been a hexagon.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHUdbKqKfBA6Dv4dnyknVoHWip3oTbl7EiXules2ZCGJKdBSYHQ2P_AvXNuNlZ2t0JsumfLcaSrd0g3Mgk3aIN5VFc1MEW_xLjsq0nCIEQlARhC9u8GRwqE7YayeVdTnMuNqxpUZrJJ2V8/s400/15.jpg)
10. Erase (delete) the lines and start coloring the stars...
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrd1EgKERTkAaEmworP6ygaCUNzubryYVMVUFg8_jTK3yDbo4ryWrzhNjpe59hm3owUHWQQ88RwaT2QkPPLb5tEeF6FG8p3eSR1KvGXnaETBSn_P7uxpW9GUG-WhPGQr9JUzslqU-Q80zE/s400/16.jpg)
11. ... and hexagons.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOVnAc2iFUp39c8Je0-sHJvf_LC5iEUtP6Ecvn9JSwT4NSFwPal7na2-bHlDPUC-joIHpThlSpRyKTd19p5nV13M40qthj8B-22EsxUKnUjIUd83ofQiq7OYf5yNyl5-WtEhFZSsY6VvpO/s400/17.jpg)
12. Finished (points were also deleted).
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiN9kPGVbOGqpH2GCA6KlpcbOrIfCGanVOjZU9Vx8QDrV2Ag3KlFICq44sZ_MQxeul6UiGNZ3LODCeTb2aWMNJQHhRPXTdw-OKPdXC_let_O07821SyGcBO-z3KJ0wV-SEfWN-gu0r25nsT/s400/18.jpg)
6 comments:
Nice!
I really loved this wonderful blog. Please keep up the good work.
mba india
Thank you for your nice comments.
What a fun Post!
Thanks!
How did you know how to do this? Did you figure it out yourself or did you learn it somplace?..Nice!
I found some good books, a long time ago, when I was teaching middle school.
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