Texas Mathematics Teachers' Bulletin . Plotting the locus for values of B from 0° to 180° we have thecurve DNOP (Fig. 5). For values of B from 180^ to 360° the re-sulting curve will be sjTnmetrical to DNOP with respect to trisect an angle make at the point P in the axis OD an anglesay NPD equal the given angle. Join N with the pole 0 thenthe angle ONP equals one-third of the given angle. Mathematics Teachers Bulletin 11 The equation of the curve in rectangular co-ordinates reduces to x-+y-—2ax=a Ax-+y- This, of course, is a higher plane curve. In plane elementarygeometry the only curves
Texas Mathematics Teachers' Bulletin . Plotting the locus for values of B from 0° to 180° we have thecurve DNOP (Fig. 5). For values of B from 180^ to 360° the re-sulting curve will be sjTnmetrical to DNOP with respect to trisect an angle make at the point P in the axis OD an anglesay NPD equal the given angle. Join N with the pole 0 thenthe angle ONP equals one-third of the given angle. Mathematics Teachers Bulletin 11 The equation of the curve in rectangular co-ordinates reduces to x-+y-—2ax=a Ax-+y- This, of course, is a higher plane curve. In plane elementarygeometry the only curves used are the straight line and circle soour problem is outside the domain of the geometry of the point,straight line and circle. PRACTICAL SOLUTION The following is an easy practical solution of the problem oftrisecting an angle. Let ABC (Fig. 6) be the angle to be trisected, ^ith B as. ^ center and any radius BC describe a semicircle CAD. Place aset square along CDG and mark from the end of a ruler a dis-tance ecjual the radius BC. Slide the ruler along the set squarekeeping the edge always on the point A. When the mark on theruler coincides with a point on the circle draw AFE the traceof the ruler in this position, then angle FBD equals one-thirdof angle ABC <ABC=<A+<E =<AFB-f <E r=(<E+<FBD)+<E =3< solution is said to be due to Archimedes but has been re-discovered several times and published accordingly up to June,1922. P. H. Underwood, Ball High School, Galveston. IS GEOMETRY A DRAG? A few years ago when there was some discussion throughcertain educational journals of that age-worn proposition ofthe trisection of any angle I was teaching a class of representa-tive ninth grade students in Plane Geometry. I rememberthat there was an unusual amount of interest in the proposi-tion manifested by members of the class. They seemed
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