Propositiones - Part 1 - Answer

I presented the problem for Part 1 here.  The answer is as follows.

The merchant would need to buy 1 boar, 9 sows, and 90 piglets.  As there are three variables and only two equations, trial and error must be employed.  My solution is as follows.

X=Number of Boars
Y=Number of Sows
Z=Number of Piglets

[Eq 1]  X+Y+Z = 100
[Eq 2] 10X+5Y+0.5Z = 100

Solving Equation 1 for Z and substituting into Equation 2 and simplifying you get the following equation.

[Eq3] 1.9X + 0.9Y = 10

This is where trial and error comes in and you get X=1, Y=9.  Back substituting into Equation 1, you get that Z=90.

Hope you had fun!

Propositiones - Part 1

Alcuin of York developed a series of mathematical problems for his students.  Many of these remain and are collected in the document entitled: Propositiones ad acuendos juvenes or Problems to sharpen the young.  This collection contains 56 problems, many of which have similar structure, along with corresponding answers.  These problems are presented by Hadley and Singmaster [1].  I thought it would be fun and educational to post some problems from time to time.  I'll modify them slightly for the audience.

Problem 5: The merchant and 100 dollars
A merchant wanted to buy 100 pigs for 100 dollars.  A boar cost 10 dollars, a sow cost 5 dollars, and a pair of piglets cost a dollar.  How many of each did the merchant buy?

Answer will be posted tomorrow.

[1] Hadley, J. and Singmaster, D. "Problems to Sharpen the Young", The Mathematical Gazette, Vol. 76, No. 475, The Use of the History of Mathematics in the Teaching of Mathematics (Mar., 1992), pp. 102-126

St. Teresa of Avila

Bernini, Ecstacy of St. Teresa, 1647–1652

Let nothing disturb thee;
Let nothing dismay thee:
All thing pass;
God never changes.
Patience attains
All that it strives for.
He who has God
Finds he lacks nothing:
God alone suffices.

Alcuin of York

Alcuin was an eminent educator, scholar, and theologian born about 735; died 19 May, 804. He came of noble Northumbrian parentage, but the place of his birth is a matter of dispute. It was probably in or near York. While still a mere child, he entered the cathedral school founded at that place by Archbishop Egbert. His aptitude, and piety early attracted the attention of Aelbert, master of the school, as well as of the Archbishop, both of whom devoted special attention to his instruction. In company with his master, he made several visits to the continent while a youth, and when, in 767, Aelbert succeeded to the Archbishopric of York, the duty of directing the school naturally devolved upon Alcuin. During the fifteen years that followed, he devoted himself to the work of instruction at York, attracting numerous students and enriching the already valuable library. While returning from Rome in March, 781, he met Charlemagne at Parma, and was induced by that prince, whom he greatly admired, to remove to France and take up residence at the royal court as "Master of the Palace School". The school was kept at Aachen most of the time, but was removed from place to place, according as the royal residence was changed. In 786 he returned to England, in connection, apparently, with important ecclesiastical affairs, and again in 790, on a mission from Charlemagne. Alcuin attended the Synod of Frankfort in 794, and took an important part in the framing of the decrees condemning Adoptionism as well as in the efforts made subsequently to effect the submission of the recalcitrant Spanish prelates. In 796, when past his sixtieth year, being anxious to withdraw from the world, he was appointed by Charlemagne Abbot of St. Martin's at tours. Here, in his declining years, but with undiminished zeal, he set himself to build up a model monastic school, gathering books and drawing students, as before, at Aachen and York, from far and near. He died 19 May, 804. Source