I loved geometry in high school. But the geometry taught did not deal with objects in three dimensions. And it was not self evident to me that if the diagonals were flat then the board had no twist. So I came up with this proof. I think Euclid would be proud . Axiom 1 Three points in space define a plane just as two points define a straight line. Axiom 2 Points are said to be co-planar if they lie on the same plane. And by definition if a board has no twist in it all the points on the surface of a board lie on the same plane Axiom 3 All points on a straight line are co-planar. Axiom 4 If a point X is co planar with point Y and point Z is co-planar with Y then X and Z are co-planar. Let A, B,C and D be the four corner of the board and E be the centre. By Axiom 1 three of the four corners of the board A,B,C define a plane . It is necessary to prove that D is co-planar with A,B,C. By observation E lies on a straight line with A and C and hence are co-planar with A and C by Axiom 3. Also by observation E lies on a straight line with B and D and also are all co-planar. Since A,B,C define a plane and are co-planar with E and D is also co-planar with E then D is co-planar with A,B,C and the board has no twist. QED
I don't think you can say that you have E on a straight line with A and C. Three of the four corners being coplanar does not prove that that the center of the board, (E,) is not convex or concave with respect to the corners.
Ha ha! Be Fore, wonderful, language is so amazing. I wonder if Jack could be a shortening of the "Jack of all trades" a popular saying in the UK i.e. not specific to any single use but can be used for many, often used to describe a versatile worker who is not a specialist. Just looked it up on wikipedia which seems to concur! Thanks Jim, just ordered Hand and Eye and Hound and Eye and very much looking forward to reading them.
Thank you for the information great extra use of an already existing tool to smooth out work flow.
Love 💓 you’re wonderful work from Australia 🇦🇺
I loved geometry in high school. But the geometry taught did not deal with objects in three dimensions. And it was not self evident to me that if the diagonals were flat then the board had no twist. So I came up with this proof. I think Euclid would be proud
.
Axiom 1 Three points in space define a plane just as two points define a straight line.
Axiom 2 Points are said to be co-planar if they lie on the same plane. And by definition if a board has no twist in it all the points on the surface of a board lie on the same plane
Axiom 3 All points on a straight line are co-planar.
Axiom 4 If a point X is co planar with point Y and point Z is co-planar with Y then X and Z are co-planar.
Let A, B,C and D be the four corner of the board and E be the centre.
By Axiom 1 three of the four corners of the board A,B,C define a plane . It is necessary to prove that D is co-planar with A,B,C.
By observation E lies on a straight line with A and C and hence are co-planar with A and C by Axiom 3.
Also by observation E lies on a straight line with B and D and also are all co-planar.
Since A,B,C define a plane and are co-planar with E and D is also co-planar with E then D is co-planar with A,B,C and the board has no twist.
QED
I don't think you can say that you have E on a straight line with A and C. Three of the four corners being coplanar does not prove that that the center of the board, (E,) is not convex or concave with respect to the corners.
i don't know why i am so surprised by this. it seems so obvious after you see it. Thank you Jim!
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super!!
This is great stuff, so that's why it's called a Plane, and why the No.7 is called a Try plane, brilliant! What about Fore and Jack I wonder?
David Fernleigh we use foreplanes to ready surfaces Before truing with the try plane. don't know jack about the jack
Ha ha! Be Fore, wonderful, language is so amazing. I wonder if Jack could be a shortening of the "Jack of all trades" a popular saying in the UK i.e. not specific to any single use but can be used for many, often used to describe a versatile worker who is not a specialist. Just looked it up on wikipedia which seems to concur! Thanks Jim, just ordered Hand and Eye and Hound and Eye and very much looking forward to reading them.