Small Comments ON EULER'S FORMULA FOR NETS Euler's topological characteristics is known to be the same (2) for a sphere and a plane. Net is on a plane so having two formulas may cause confusion. When we cut a NET an infinitely big piece is left over. It must be counted as a face. Then we will have the same Euler's formula with 2 in its right side. So there is one formula: V+F-E=2. For Nets, we should count also the additional outer piece as a face. But if we do not want to count it for Nets then we should formally replace 2 with THE BEST PROTRACTOR IS A CLOCK FACE - it is divided into 60 equal 1-degree angles! VERTICAL-HANG PROTRACTOR for slope measuring can be made easier, if, instead of hanging a string from a protractor's hole with a heavy washer or something else, we hang an opened up Jumbo paper CLIP. Put it through the hole - it will be perfectly vertical. ON THE TRIANGLE CONGRUENCY In SsA version, if the Side opposite to the given (interior) angle A is larger, then the triangles are congruent A PERFECT PRODUCTION I sketched on the overhead transparecy a semicircle and drew by hand an angle as I said 30 degrees, for example. Then I put over it a Narrow Diamond Piece to show how they can use pieces to construct that angle. It matched exactly. WOW,- I said: "...this piece is manufactured perfectly! See how it fits". QUANTITIES IN RELATIONS GENERALIZING RULES OF ARITHMETICS: each such variable cancels out, and the relation is simplified, usually reduced to a trivial numerical TRUTH: identity (like 0=0), or inequality (like 1>0). TOPOLOGY OF LINEAR SYSTEMS A SYSTEM OF LINEAR EQUATIONS CAN BE SOLVED IF AND ONLY IF THERE IS NO TOPOLOGICALLY CLOSED LOOP WITH EVEN NUMBER OF SIDES (RELATIONS). NAKED BUT ARMED After one presantations of my surprise Trick "What's In The Bag? With ONE Question!", a Lady approached me and said: - As I prepared to read my answer all of a sudden I felt like NAKED... - Naked but armed... Send your comments to mamikon@caltech.edu