9884 Players currently online!
Man vs. Machine - good luck!
Turn-based games at any time!
Vote for the best move to win!
Do you have what it takes?
Sharpen your tactical vision!
Get advice and game insights!
Learn from top players & pros!
View millions of master games!
Your virtual chess coach!
Perfect your opening moves!
Test your skills vs. computer!
Find the right private coach!
Can you solve it each day?
Bring it all together!
Beginners, start here!
Make friends & play team games!
News from the world of chess!
Search all Chess.com members!
Find local clubs & events!
Who's the best of your friends?
Read what members are saying!
Lorenzo Mascheroni (May 13, 1750 – July 14, 1800) was an Italian mathematician. He was born near Bergamo, Lombardy. At first mainly interested in the humanities (poetry and Greek language), he eventually became professor of mathematics at Pavia. In his Geometria del Compasso (Pavia, 1797), he proved that any geometrical construction which can be done with compass and straightedge, can also be done with compasses alone. However, the priority for this result (now known as the Mohr-Mascheroni theorem) belongs to the Dane Georg Mohr, who had previously published a proof in 1672.
Mascheroni construction for the Pentagon
1) Draw circle A. Find B, a random point on circle A. 2) Draw a circle at B with radius BA. Circle B intersects circle A at C. 3) Draw a circle at C with radius CA. Circle C intersects circle A at D. 4) Draw a circle at D with radius DA. Circle D intersects circle A at E. 5) Draw a circle at B with radius BD and draw a circle at E with radius EC. They intersect at F. 6) Draw a circle at A with radius AF. This new circle intersects circle B at G. 7) Draw a circle at G with radius GB. Circle G intersects circle A at H. 8) Draw a circle at H with radius HG. Circle H intersects circle A at points I and J. 9) Draw two circles, one each at I and J, each with radii ID and JC. They intersect at K. 10) Draw a circle at B, this time with radius BK. This circle intersects circle A at points L and M. B,L,M are points of the pentagon. Through them the other two can be found.
Mascheroni construction for the Hexagon
Simply draw a circle and choose a point on that circle (yellow). Then draw a circle centered at that point of identical radius. Where that circle intersects the original circle, draw two more circles of equal radius. Continue doing this until you get 6 points on the circle. Those are the 6 points of the hexagon.
I keep asking myself (civil engineer, 84) about the joy for mathematics that today youth might have in the future due to the absorbing power of cybernetics (computers and similar).
Wanted: Good opening lines !
by Chessaddictedprakhar 3 minutes ago
Crazy Streaks on Tactics Trainer
by Samsch 5 minutes ago
A jam-packed position, please help!!
by jayantjpr 5 minutes ago
by shdu02 6 minutes ago
Do top GMs use drugs to boost their play?
by ja734 7 minutes ago
Becoming a Master with Diamond Premium Membership?.
by cdowis75 9 minutes ago
4/14/2014 - The Good Old Trick
by BryanCFB 11 minutes ago
by XavierPadilla 13 minutes ago
Attention Mayank Shridhar
by Chessaddictedprakhar 14 minutes ago
My unlukiest loss due to internet connectivity
by bhoopalan 15 minutes ago
Why Join | Chess Topics |
Help & Support |
© 2014 Chess.com
• Chess - English
We are working hard to make Chess.com available in over 70 languages. Check back over the year as we develop the technology to add more, and we will try our best to notify you when your language is ready for translating!