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It Is with More Than Passing Pleasure That I Recall the Fine Courtesy, The THE ROCKY MOUNTAIN SECTION OF THE ASSOCIATION. 281 It is with morethan passingpleasure that I recall the finecourtesy, the generosity,the extrememodesty and the enthusiasmexhibited by FrereGabriel Marie in occasionalcorrespondence during the past decade. R. C. ARCHIBALD. BROWN UNIVERSITY, March 23, 1917. FIRST REGULAR MEETING OF THE IOWA SECTION. The firstregular meeting of the Iowa Sectionof The MathematicalAssociation of Americawas held at GrinnellCollege, Grinnell, Iowa, on April28, 1917,and the followingprogram given: (1) "A unifiedcourse for Freshmanmathematics:" by ProfessorR. B. MCCLENON,Grinnell College. Leader of the discussion: ProfessorJULIA COLPITTS, Iowa State College. (2) "The foundationof Freshmanmathematics in technicalschools:" by Dean E. W. STANTON,Iowa StateCollege. In hisabsence, the paper was read by Professor.MARIA ROBERTS, Iowa State College. Leadersof the discussion: ProfessorsJ. F. REILLY, Iowa State University,and C. W. EMMONS,Simpson College. (3) "{Puttinglife into dry bones:" by ProfessorF. M. MCGAW,Cornell College. Leadersof the discussion: Professors W. J.RusE, GrinnellCollege, and W. E. BECK,Iowa State University. The followingalso took part in the discussions:Professors Weston, Trow- bridge,Stewart and Neff. All the paperswere good and the discussionswere to the pointshowing a keeninterest in the sortof a programoffered. The action at the businesssession in planningtwo meetingseach yearalso indicatessome- thingof the interesttaken in the Iowa Section. The attendanceincluded some twentymembers of the Associationand otherswho will become members in due course. The followingofficers were elected for the ensuingyear: I. F. NEFF, Drake University,Chairman; R. B. MCCLENON, GrinnellCollege, Vice-Chairman; W. E. BECK, Iowa State University,Secretary. G. A. CHANEY, I. F. NEFF, Chairman, Secretary-Treasurer. THE ROCKY MOUNTAIN SECTION OF THE ASSOCIATION. In September,1916, it was suggestedto Dr. G. H. Light,of the University ofColorado, that a sectionof The MathematicalAssociation of America be formed to includethe states of Wyoming and Colorado. The suggestionwas actedupon and as a resulta meetingwas called at the Universityof Coloradoon April7, 1917. This content downloaded from 158.142.128.179 on Sun, 11 Jan 2015 19:26:12 PM All use subject to JSTOR Terms and Conditions 282 THE KENTUCKYSECTION OF THE ASSOCIATION. The meetingwas a great successand the Rocky MountainSection of the Associationwas formedwith the following officers: C. B. Ridgaway,Professor of Mathematics,University of Wyoming,Chairman. C. C. VanNuys,Professor of Physics,Colorado School of Mines, Vice-Chairman.G. H. Light,Assistant Professorof Mathematics, University of Colorado,Secretary-Treasurer. Papers werepresented by 0. C. Lester,Professor of Physics,University of Colorado,on "The SolidAngle," and FlorianCajori, Professor of Mathematics, ColoradoCollege, on "Fluxions." Discussionof thesepapers was general. Therewere twenty-one present at the meeting,fifteen of whomare already membersof the Associationand the otherswill join at once: C. B. RIDGAWAY, Professorof Mathematics,C. E. STROMQUIST,Professor of Mathematics,J. C. FITTERER,Professor of Civil Engineering, University of Wyoming; C. R. BURGER, Professorof Mathematics, G. E. F. SHERWOOD,Assistant Professorof Mathe- matics, C. C. VANNUYS,Professor of Physics, H. M. SHOWMAN,Assistant Pro- fessor of Civil Engineering,F. W. LUCHT, Assistant Professorof Mechanical Engineering,W. J. HAZARD,Assistant Professor of Mechanical Engineering, ColoradoSchool of Mines; S. L. MACDONALD,Professor of Mathematics,Colorado A. & M. College; G. W. FINLEY, Professorof Mathematics,Colorado State Teacher'sCollege; FLORIAN CAJORI, Professor of Mathematics,Colorado College; W. H. HILL, GreeleyHigh School; E. L. BROWN,East Denver High School; I. M. DELONG, Professorof Mathematics, G. H. LIGHT,Assistant Professor of Mathematics,CLARIBEL KENDALL, Instructor in Mathematics,0. C. LESTER, Professorof Physics, J. W. WOODROW,Assistant Professor of Physics, DR. 0. A. RANDOLPH,Instructor in Physics,C. E. SPERRY,Assistant Professor of Mathe- matics,University of Colorado. G. H. LIGHT, Secretary-Treasurer. THE KENTUCKY SECTION OF THE ASSOCIATION. The MathematicsSection of the Associationof KentuckyColleges and Universities(now the KentuckySection of the MathematicalAssociation of America)was organizedin April,1909, and sincethen has metregularly twice a year. This organizationhas directedmost of its attentionto a considerationof problemspeculiar to collegiatework, one resultof whichhas been a tendency towarda standardizationof the mathematicalcourses in the collegesof the state. Anotherfeature of the workof this organizationhas been the consistent effortsput forthto strengthenand improvethe teachingof mathematicsin the highschools of the state. It was at firstplanned to workout a correlatedcourse in mathematicsfor the high schools but this was laterabandoned. In 1910it was decidedto testthe degreeof preparationof all studentsentering the collegesof thestate by settingexaminations covering algebra and planeand solidgeometry. This content downloaded from 158.142.128.179 on Sun, 11 Jan 2015 19:26:12 PM All use subject to JSTOR Terms and Conditions 252 THE ROCKY MOUNTAIN SECTION. elements. Hence the midpointMk of the innersegment liIj correspondsto the ideal point of the line ilj. From this it followsthat theideal line of theplane transformsinto a conic througheach of the midpointsof the siX segmentsllj in additionto passing throughA, B and C, as noted above. We may now show that thisconic is a circle. If P is an ideal point the lines a and b joiningit to two of the mirrorsare parallel. Then the sum of the angles a, ,Band 'y is fourright angles. Now as P moves on the ideal line a change in a A a' P' FIG. 3. the angle a is accompanied by a change in the angle ,Bof the same magnitude but opposite in sign. Then a + ,Bis constant and hence 'y = 360? - (a + ,B) is constantand P' moves on a circle. It follows,then, that theconic obtainedby transformingthe ideal line of theplane is the nine-pointcircle of each of thefour trianglesIiljlk. THE ROCKY MOUNTAIN SECTION. The secondannual meetingof the Rocky Mountainsection of the Mathe- maticalAssociation of America was heldat Laramie,Wyoming, under the auspices ofthe University of Wyoming, March 29 and 30, 1918. The meetingopened with a dinnerin HoitHall at 6 P. M., at whichthe address of welcomeby ActingPresident Nelson of theUniversity of Wyomingand the responseby Professor0. C. Lester,of theUniversity of Colorado,were given. Afterthe dinner, an adjournmentto the administrationbuilding was made and thefollowing program was carriedout: 1. Special Coursesin Mathematicsfor Technical Students. PROFESSORS. L. MACDONALD,Colorado A. & M. College, Ft. Collins. 2. The Theory of the Mercury Arc. PROFESSORJ. W. WOODROW,University ofColorado, Boulder. 3. The LengthIntegral in the non-EuclideanWorld of Poincare. PROFESSOR C. E. STROMQUIST,University of Wyoming, Laramie. The purposeof this paper was to derivean integralfor length in the non- Euclideanworld proposed by Poincarein his "Foundationsof Science,"English translationby Halsted,page 75. The shortestdistance between two pointsis This content downloaded from 158.142.128.179 on Tue, 13 Jan 2015 21:59:31 PM All use subject to JSTOR Terms and Conditions THE ROCKY MOUNTAIN SECTION. 253 assumed to be the circlethrough these points and perpendicularto the boundary sphere. The general formof the length integralunder this assumptionis then worked out for the case of the plane. Under the furtherrestriction that trans- versals are perpendicularto their extremals,the length integral along a curve y = f(x) between two points, P(xi, yi) and P(x2, y2), reduces to the form 1z2+,T _R2 dx, wherep = dy/dxand R is the radius of the boundarysphere. 4. The Trend Curve for the Price of Copper. PROFESSOR C. S. SPERRY, Uni- versityof Colorado, Boulder. 5. A Problem in Geometry. MR. J. Q. McNATT, Colorado Fuel & Iron Co., Florence. The author gave a new proof for the relation between the side of a regular inscribedpentagon and the side of a regularinscribed decagon. 6. Some Systems of Coordinates. PROFESSOR G. H. LIGHT, University of Colorado, Boulder. This paper dealt principallywith intrinsicco6rdinates and showed the ex- tremelysimple form that the equations of some well-knowncurves and their evolutes assume when expressedin termsof these coordinates. 7. Mathematics at the Front. MR. W. H. HILL, GreeleyHigh School, Greeley. 8. Some Functions of Solid Angles. PROFESSOR J. C. FITTERER, Universityof Wyoming,Laramie. 9. The Origin of the name "Rolle's Curve." The Origin of the name "Mathe- matical Induction." PROFESSOR FLORIAN CAJORI, Colorado College, Colorado Springs. The second of these papers by ProfessorCajori appeared in the Mav num- ber of this MONTHLY;the firstwill appear in a later issue. 10. The Sine and Cosine Integrals f sin x/x dx and f cos x/xdx in Electromag- netism. PROFESSOR C. C. VANNUYS, Colorado School of Mines, Golden. This paper deals withinteresting physical applications of the functionsknown to mathematiciansas the sine and cosine integrals. One of the problemsdealt with is that of determiningthe equivalent resistance and inductance due to radiation of electromagneticwaves of a long straightconductor carrying a har- monicalternating current of singlefrequency such as is employedin the oscillation circuitsused in radio telegraphy. Another problem discussed is that of the electromotiveforce induced in a straightvertical conductorby an oscillatorycurrent
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