Here is the link.

keywords:

[unknown caller]

[mystery]

# Day: April 29, 2020

# teaching of elementary mathematics

“The human mind is so constructed that it must see every perception in a time-relation—in an order—and every perception of an object in a space-relation—as outside or beside our perceiving selves. These necessary time-relations are reducible to Number, and they are studied in the theory of number, arithmetic and algebra. These necessary space-relations are reducible to Position and Form, and they are studied in geometry. Mathematics, therefore, studies an aspect of all knowing, and reveals to us the universe as it presents itself, in one form, to mind. To apprehend this and to be conversant with the higher developments of mathematical reasoning, are to have at hand the means of vitalizing all teaching of elementary mathematics.”

— Nicholas Murry Butler

cf:

“Nothing is of greater importance than the early instruction of youth.”

— Peter Stuyvesant

keywords:

[education]

[instruction]

[training]

[learning]

[study]

[curriculum]

[educator]

# online book: Mathematical Excursions to the World’s Great Buildings

(345 pages)

Here is the link.

This book contains an introduction to Calculus, and a Glossary of Architectural Terms.

Chapter Headings

1. Humanity Awakening: Sensing Form and Creating Structures

2. Greek Geometry and Roman Engineering

3. Architecture Inspired by Faith

4. Transmission of Mathematics and Transition in Architecture

5. The Renaissance: Architecture and the Human Spirit

6. A New Architecture: Materials, Structural Analysis, Computers and Design

7. Basic Calculus and Its Application to the Analysis of Structures

keywords:

[geometry]

[survey]

[tour]

# the derivative

the derivative

[Mathematics]

[Calculus]

[limit]

[rate of change]

# obtaining the tangent via the secant

obtaining the tangent via the secant

keywords:

[Mathematics]

[Calculus]

[limit]

[Geometry]

# the tangent to a curve at a point

the tangent to a curve at a point

keywords:

[Mathematics]

[Calculus]

[Geometry]

# OBSERVATION (pronunciation)

Pronunciation is rooted in semantics.

keywords:

[text-to-speech technology]

[Linguistics]

[Language Arts]

[intonation]

# Fermat’s polygonal number theorem

Here is the link to the Wikipedia article on this topic.

Note that Lagrange’s four-square theorem is a special case of Fermat’s polygonal number theorem.

keywords:

[Mathematics]

[Number Theory]

[b^2 < 4a]

[3a < b^2 + 2b + 4]

see also:

[‘regular’ polygonal numbers]

[n-gonal numbers]

[additive basis of order n]

# centered polygonal numbers

Here is the link to the Wikipedia article on this topic.

– not to be confused with ‘regular’ polygonal numbers.

keywords:

[Mathematics]

[Number Theory]

see also:

[‘regular’ polygonal numbers]

# polygonal numbers

Here is the link to the Wikipedia article on this topic.

aka ‘regular polygonal numbers’, since ‘centered’ polygonal numbers also exist.

keywords:

[Mathematics]

[Number Theory]

[backronym]

see also:

[centered polygonal numbers]