Includes bibliographical references (pages 179-181) and index.

Introduction : Exercise of a skill ; A career in mathematics ; Teaching mathematics ; Spiritual values ; Philosophy -- The texture of beauty : Ancient standing ; Appreciation, given and acquired ; Definitions ; Evolution of aesthetic faculty ; Plato, Croce, Wordsworth, Coleridge ; Unity in variety ; Working hypothesis ; Structure of the psyche ; Emotional activity ; Aesthetics ; Music ; Aesthetic pleasure universal ; Creative activity: empathy -- The divine proportion : Pythagoras and numbers: music and integers ; The golden section (Euclid) ; Phidias and the Parthenon ; Phi (x), numerical value ; Geometrical determination of Phi ; Pentagram or triple triangle: a symbol ; Iamblichus and the Pythagorean brotherhood ; The five Platonic solids -- Analysis of beauty : Surprise, wonder, curiosity: an example ; Status of Phi: mathematical reality ; Mathematics, a language ; Ubiquity of Phi ; Phi in trigonometry: multiples of 18° ; The golden triangle ; Exercises -- Phi and fi-Bonacci : Additive series ; Computer calculation of Phi ; Geometric fallacy ; The golden series: remarkable properties ; Aesthetic claim ; Divine proportion and major sixth ; Estimation of pitch ; Summary ; Binet's formula ; The law of growth -- Art and the golden rectangle : Aesthetic sensibility, inborn and acquired ; "Beauty is a word of God" ; Definitions ; The divine proportion ; Experimental aesthetics (Fechner, Witmar, Lalo, Thorndike) ; The golden ellipse ; The German DIN ; Additive squares ; Rectangular spiral -- Beauty in mathematics : Ambiguity in title ; Clarified by an example: the parabola ; The aesthetically ungifted ; Beauty a guide to truth ; Ideas in poetry and mathematics ; Evolution of aesthetic feeling ; Mathematics and music ; Why is recollection pleasurable? ; Ingredients of beauty ; Alternation of tension and relief ; Realization of expectation ; Surprise ; Perception of unsuspected relationships ; Patterns ; Brevity ; Unity in variety ; Sensuous pleasure from curves ; Wonder, awe, mystery ; The seeing eye -- Simple examples of aesthetic interest : A limited anthology ; The pill maker ; Triangle limited by the golden ratio ; Triangle inscribed in a rectangle ; The cross of Lorraine ; The golden cuboid ; Logarithmic spiral -- Further examples : Motives in teaching mathematics ; Trisectors of an angle ; Phi: another hiding place ; Tetrahedron problem ; Two triangles ; Logarithm of the golden mean ; Phi and the parabola ; Golden and conic sections -- Patterns : A source of aesthetic pleasure ; Chess problems ; Euler's formula ; Magic squares (a Fibonacci magic square) ; Polygonal numbers ; Fermat's rules --Pascal's triangle and Fibonacci : Pascal's triangle ; Chinese triangle ; Probability computation ; More Pascal patterns ; Continued fractions ; Convergents and the Fibonacci series -- The Fibonacci numbers : Relation to golden ratio ; Source of aesthetic feeling ; First forty golden numbers ; Fibonacci series: a geometrical progression ; A practical problem ; Binet's formula ; Some properties of the Fibonacci sequence ; Zero-value determinants -- Nature's golden numbers : A poet's view refuted ; Teleology ; Fibonacci and nature ; Multiple reflections ; Fibonacci and the atom ; Leonardo of Pisa ; The rabbit problem ; The bee hive: genealogy of the drone bee ; Phyllotaxis: leaf divergence and petal numbers -- Spira mirabilis : The equiangular spiral: the sunflower ; Sea shells ; Expressive lines ; X-ray picture of the nautilus ; Various designations ; Gnomons: D'Arcy Thompson and the law of growth ; The golden triangle ; Polar equation of spiral ; Musical scale and the spiral ; Conclusion.

Engaging introduction to that curious feature of mathematics which provides framework for so many structures in biology, chemistry, and the arts. Discussion ranges from theories of biological growth to intervals and tones in music, Pythagorean numerology, conic sections, Pascal's triangle, the Fibonnacci series and much more.