An Ideal History of Experiments on the Regular 
Pentagon.* 
A Pedagogical Essay. 
By H. Y. BENEDICT. 
Mathematics may be regarded from three fairly distinct points of 
view: 
1. As a department of pure knowledge, having a philosophical and 
aesthetic valne of its own, unrelated to other sciences or to utility. 
2. As a servant of other sciences, pure and applied. 
3. In its elementary branches, as a mental gymnasium wherein the 
youthful mind may be taught to reason soundly. 
In order, these are the views of the pure mathematician, the scientist, 
and the teacher. Every one will admit the justice of each view, but will 
emphasize one at the expense of the others in accordance with personal 
taste and training. Yet so closely connected are these views that no 
advance in pure mathematics can occur without being accompanied by 
a corresponding advance in mathematical applications and, to a less 
extent, in mathematical teaching. 
In recent years, if the platitude be allowable, the activity of pure 
mathematician, scientist, and teacher has been remarkable. The founda- 
tions of mathematics have been and are being very carefully scrutinized. 
The axioms and postulates of elementary geometry and algebra have been 
subjected to a criticism that requires some maturity and acuteness to 
appreciate, and to a revision that has an important bearing on the teach- 
ing of these subjects. Already our text-books are beginning to show some 
of the good effects of this revision, and one of the most encouraging 
signs of the times is the increasing interest of competent pure mathe- 
maticians in elementary instruction and in elementary texts. To Pro- 
fessor Moore, of the University of Chicago, much credit is due. Him- 
self a pure mathematician and a teacher of advanced students, he is 
using his great knowledge and influence to bring about needed changes 
in elementary instruction. In England, Professor Perry and others are 
carrying on an active and radical reform movement, but are being stub- 
bornly opposed by the almost stupid conservatism of the schoolmasters. 
*This paper was read at the regular formal meeting of the Texas Academy of 
Science in June, 1903. 
