animated
Animation is a method by which still figures are manipulated to appear as moving images. In traditional animation, images are drawn or painted by hand on transparent celluloid sheets to be photographed and exhibited on film. Today, most ani ...
-
live-action
Live action (or live-action) is a form of cinematography or videography that uses photography instead of animation. Some works combine live-action with animation to create a live-action animated film. Live-action is used to define film, video ...
featurette
In the American film industry, a featurette is a kind of film that is shorter than a full-length feature, but longer than a short film. The term may refer to either of two types of content: a shorter film or a companion film.
Medium-length fil ...
produced by
Walt Disney Productions
The Walt Disney Company, commonly known as Disney (), is an American multinational mass media and entertainment conglomerate headquartered at the Walt Disney Studios complex in Burbank, California. Disney was originally founded on October 1 ...
and featuring
Donald Duck
Donald Fauntleroy Duck is a cartoon character created by The Walt Disney Company. Donald is an anthropomorphic white duck with a yellow-orange bill, legs, and feet. He typically wears a sailor shirt and cap with a bow tie. Donald is known fo ...
Joshua Meador
Joshua Lawrence "Josh" Meador (March 12, 1911 - August 24, 1965) was an American animator, effects animator, special effects artist, and animation director for the Walt Disney studios.
Biography
Meador was born in Greenwood, Mississippi. His ...
as sequence directors) and was released on June 26, 1959. It was nominated for an
Academy Award
The Academy Awards, better known as the Oscars, are awards for artistic and technical merit for the American and international film industry. The awards are regarded by many as the most prestigious, significant awards in the entertainment ind ...
Donald Duck
Donald Fauntleroy Duck is a cartoon character created by The Walt Disney Company. Donald is an anthropomorphic white duck with a yellow-orange bill, legs, and feet. He typically wears a sailor shirt and cap with a bow tie. Donald is known fo ...
, holding a hunting rifle, passing through a doorway to find that he has entered Mathmagic Land. This "mighty strange" fantasy land contains trees with
square root
In mathematics, a square root of a number is a number such that ; in other words, a number whose '' square'' (the result of multiplying the number by itself, or ⋅ ) is . For example, 4 and −4 are square roots of 16, because .
...
s, a stream flowing with
number
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual number ...
s, and a walking pencil that plays
tic-tac-toe
Tic-tac-toe (American English), noughts and crosses (Commonwealth English), or Xs and Os (Canadian or Irish English) is a paper-and-pencil game for two players who take turns marking the spaces in a three-by-three grid with ''X'' or ''O''. ...
. A geometric bird recites (almost perfectly) the first 15 digits of pi. Donald soon hears the voice of the unseen "True Spirit of Adventure" (
Paul Frees
Solomon Hersh "Paul" Frees (June 22, 1920November 2, 1986) was an American actor, comedian, impressionist, and vaudevillian. He is known for his work on Metro-Goldwyn-Mayer, Walter Lantz, Rankin/Bass, and Walt Disney theatrical cartoons during ...
), who will guide him on his journey through "the wonderland of mathematics".
2: The Time Of Pythagoras
Donald is initially not interested in exploring Mathmagic Land, believing that math is just for " eggheads". When "Mr. Spirit" suggests a connection between math and music, though, Donald is intrigued. First, Donald discovers the relationships between
octave
In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...
s and string length which develop the
musical scale
In music theory, a scale is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is an ascending scale, and a scale ordered by decreasing pitch is a descending scale.
Often, especially in the ...
of today. Next, Donald finds himself in
ancient Greece
Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity ( AD 600), that comprised a loose collection of cu ...
, where
Pythagoras
Pythagoras of Samos ( grc, Πυθαγόρας ὁ Σάμιος, Pythagóras ho Sámios, Pythagoras the Samian, or simply ; in Ionian Greek; ) was an ancient Ionian Greek philosopher and the eponymous founder of Pythagoreanism. His poli ...
and his contemporaries are discovering these same relationships. Pythagoras (on the
harp
The harp is a stringed musical instrument that has a number of individual strings running at an angle to its soundboard; the strings are plucked with the fingers. Harps can be made and played in various ways, standing or sitting, and in orc ...
), a
flute
The flute is a family of classical music instrument in the woodwind group. Like all woodwinds, flutes are aerophones, meaning they make sound by vibrating a column of air. However, unlike woodwind instruments with reeds, a flute is a reedles ...
player, and a
double bass
The double bass (), also known simply as the bass () (or #Terminology, by other names), is the largest and lowest-pitched Bow (music), bowed (or plucked) string instrument in the modern orchestra, symphony orchestra (excluding unorthodox addit ...
player hold a "
jam session
A jam session is a relatively informal musical event, process, or activity where musicians, typically instrumentalists, play improvised solos and vamp over tunes, drones, songs, and chord progressions. To "jam" is to improvise music without ...
" which Donald joins after a few moments using a
vase
A vase ( or ) is an open container. It can be made from a number of materials, such as ceramics, glass, non-rusting metals, such as aluminium, brass, bronze, or stainless steel. Even wood has been used to make vases, either by using tree species ...
as a
bongo drum
Bongos ( es, bongó) are an Afro-Cuban percussion instrument consisting of a pair of small open bottomed hand drums of different sizes. They are struck with both hands, most commonly in an eight-stroke pattern called ''martillo'' (hammer). The ...
. Pythagoras' mathematical discoveries are, as the Spirit explains, the basis of today's music, and that music would not exist without "eggheads". The segment ends with a sequence of
live action
Live action (or live-action) is a form of cinematography or videography that uses photography instead of animation. Some works combine live-action with animation to create a live-action animated film. Live-action is used to define film, video ...
musicians playing both
jazz
Jazz is a music genre that originated in the African-American communities of New Orleans, Louisiana in the late 19th and early 20th centuries, with its roots in blues and ragtime. Since the 1920s Jazz Age, it has been recognized as a m ...
and
classical music
Classical music generally refers to the art music of the Western world, considered to be distinct from Western folk music or popular music traditions. It is sometimes distinguished as Western classical music, as the term "classical music" al ...
and Pythagoras' pals fading away.
3: The Golden Rectangle
After shaking hands with Pythagoras, who then vanishes, Donald finds on his hand a
pentagram
A pentagram (sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed star polygon, formed from the diagonal line segments of a convex (or simple, or non-self-intersecting) regular pentagon. Drawing a circle arou ...
, the symbol of the secret Pythagorean society. The Spirit then shows Donald how the mysterious golden section appears in the pentagram. Next, the pentagram is shown to contain the pattern for constructing golden rectangles many times over. According to the Spirit, the golden rectangle has influenced both ancient and modern cultures in many ways. Donald then learns how the golden rectangle appears in many ancient buildings, such as the
Parthenon
The Parthenon (; grc, Παρθενών, , ; ell, Παρθενώνας, , ) is a former temple on the Athenian Acropolis, Greece, that was dedicated to the goddess Athena during the fifth century BC. Its decorative sculptures are considere ...
Mona Lisa
The ''Mona Lisa'' ( ; it, Gioconda or ; french: Joconde ) is a half-length portrait painting by Italian artist Leonardo da Vinci. Considered an archetypal masterpiece of the Italian Renaissance, it has been described as "the best kno ...
'' and various sculptures such as the ''
Venus de Milo
The ''Venus de Milo'' (; el, Αφροδίτη της Μήλου, Afrodíti tis Mílou) is an ancient Greek sculpture that was created during the Hellenistic period, sometime between 150 and 125 BC. It is one of the most famous works of ancient ...
'' contain several golden rectangles. The use of the golden rectangle is found in modern architecture, such as the United Nations building in
New York City
New York, often called New York City or NYC, is the List of United States cities by population, most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the L ...
. Modern painters have also rediscovered the magic of the golden rectangles.
4: Mathematical Forms In Nature
The Spirit shows Donald how the golden rectangle and pentagram are related to the human body and nature, respectively. The human body contains the "ideal proportions" of the golden section; Donald, overinterpreting the Spirit's advice, tries to make his own body fit such a proportion, but his efforts are to no avail; he ends up "all pent up in a
pentagon
In geometry, a pentagon (from the Greek πέντε ''pente'' meaning ''five'' and γωνία ''gonia'' meaning ''angle'') is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°.
A pentagon may be sim ...
". The pentagram and pentagon are then shown to be found in many flowers and animals, such as the petunia, the
star jasmine
''Trachelospermum jasminoides'' is a species of flowering plant in the family Apocynaceae, native to eastern and southeastern Asia ( Japan, Korea, southern China and Vietnam).Flora of China''Trachelospermum jasminoides''/ref> Common names i ...
, the
starfish
Starfish or sea stars are star-shaped echinoderms belonging to the class Asteroidea (). Common usage frequently finds these names being also applied to ophiuroids, which are correctly referred to as brittle stars or basket stars. Starfish a ...
, the waxflower, and with the help of the inside of a
nautilus
The nautilus (, ) is a pelagic marine mollusc of the cephalopod family Nautilidae. The nautilus is the sole extant family of the superfamily Nautilaceae and of its smaller but near equal suborder, Nautilina.
It comprises six living species in ...
shell, the Spirit explains that the magic proportions of the golden section are often found in the
spiral
In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point.
Helices
Two major definitions of "spiral" in the American Heritage Dictionary are:
chess
Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to dist ...
,
baseball
Baseball is a bat-and-ball sport played between two teams of nine players each, taking turns batting and fielding. The game occurs over the course of several plays, with each play generally beginning when a player on the fielding t ...
,
American football
American football (referred to simply as football in the United States and Canada), also known as gridiron, is a team sport played by two teams of eleven players on a rectangular field with goalposts at each end. The offense, the team wi ...
,
basketball
Basketball is a team sport in which two teams, most commonly of five players each, opposing one another on a rectangular Basketball court, court, compete with the primary objective of #Shooting, shooting a basketball (ball), basketball (appr ...
,
hopscotch
Hopscotch is a popular playground game in which players toss a small object, called a lagger, into numbered triangles or a pattern of rectangles outlined on the ground and then hop or jump through the spaces and retrieve the object. It is a ch ...
Tiddlywinks
Tiddlywinks is a game played on a flat felt mat with sets of small discs called "winks", a pot, which is the target, and a collection of squidgers, which are also discs. Players use a "squidger" (nowadays made of plastic) to shoot a wink in ...
, but the Spirit does not pursue this option. Themes of Lewis Carroll's 1871 novel ''
Through the Looking-Glass
''Through the Looking-Glass, and What Alice Found There'' (also known as ''Alice Through the Looking-Glass'' or simply ''Through the Looking-Glass'') is a novel published on 27 December 1871 (though indicated as 1872) by Lewis Carroll and the ...
'' are scattered throughout the chess scene; Carroll himself was both a writer and a
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
. The extended
billiards
Cue sports are a wide variety of games of skill played with a cue, which is used to strike billiard balls and thereby cause them to move around a cloth-covered table bounded by elastic bumpers known as .
There are three major subdivisions ...
scene, which features a non-speaking live actor, shows the calculations involved in the game's "diamond system", and Donald finally learns how to do the calculations, though he ends up making it tough for himself, spectacularly hitting ten cushions in a single shot nonetheless.
6: Mathematical Thinking
The Spirit then asks Donald to play a mental game, but he finds Donald's mind to be too cluttered with "Antiquated Ideas", "Bungling", "False Concepts", "Superstitions", and "Confusion". After some mental house-cleaning, Donald plays with a
circle
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is cons ...
and a
triangle
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC.
In Euclidean geometry, any three points, when non- colline ...
in his mind, he spins them to make them respectively into a
sphere
A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the c ...
and a
cone
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.
A cone is formed by a set of line segments, half-lines, or lines con ...
, and then he discovers useful inventions such as the
wheel
A wheel is a circular component that is intended to rotate on an axle bearing. The wheel is one of the key components of the wheel and axle which is one of the six simple machines. Wheels, in conjunction with axles, allow heavy objects to be ...
,
train
In rail transport, a train (from Old French , from Latin , "to pull, to draw") is a series of connected vehicles that run along a railway track and transport people or freight. Trains are typically pulled or pushed by locomotives (often ...
,
magnifying glass
A magnifying glass is a convex lens that is used to produce a magnified image of an object. The lens is usually mounted in a frame with a handle. A magnifying glass can be used to focus light, such as to concentrate the sun's radiation to c ...
,
drill
A drill is a tool used for making round holes or driving fasteners. It is fitted with a bit, either a drill or driver chuck. Hand-operated types are dramatically decreasing in popularity and cordless battery-powered ones proliferating due to ...
,
spring
Spring(s) may refer to:
Common uses
* Spring (season), a season of the year
* Spring (device), a mechanical device that stores energy
* Spring (hydrology), a natural source of water
* Spring (mathematics), a geometric surface in the shape of a h ...
,
propeller
A propeller (colloquially often called a screw if on a ship or an airscrew if on an aircraft) is a device with a rotating hub and radiating blades that are set at a pitch to form a helical spiral which, when rotated, exerts linear thrust upon ...
, and
telescope
A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally meaning only an optical instrument using lenses, curved mirrors, or a combination of both to obse ...
. Donald then discovers that pentagrams can be drawn inside each other indefinitely. Therefore, numbers provide an avenue to consider the infinite. The Spirit states that scientific knowledge and technological advances are unlimited, and the key to unlocking the doors of the future is mathematics. By the end of the film, Donald understands and appreciates the value of mathematics. The film closes with a quotation from
Galileo Galilei
Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He ...
: "Mathematics is the alphabet with which God has written the universe".
Donald Duck
Donald Fauntleroy Duck is a cartoon character created by The Walt Disney Company. Donald is an anthropomorphic white duck with a yellow-orange bill, legs, and feet. He typically wears a sailor shirt and cap with a bow tie. Donald is known fo ...
(voice)
*
Paul Frees
Solomon Hersh "Paul" Frees (June 22, 1920November 2, 1986) was an American actor, comedian, impressionist, and vaudevillian. He is known for his work on Metro-Goldwyn-Mayer, Walter Lantz, Rankin/Bass, and Walt Disney theatrical cartoons during ...
as The True Spirit of Adventure / Narrator (voice), and the Pi creature (voice)
* June Foray as the Chess Queen (voice)
*
Daws Butler
Charles Dawson Butler (November 16, 1916May 18, 1988) was an American voice actor. He worked mostly for the Hanna-Barbera animation production company where he originated the voices of many familiar characters, including Yogi Bear, Huckleberry H ...
as the Chess King (voice)
* Roman Yanez as The Billiards Player
Production
The film was directed by Hamilton Luske. Contributors included
Disney
The Walt Disney Company, commonly known as Disney (), is an American multinational mass media and entertainment conglomerate headquartered at the Walt Disney Studios complex in Burbank, California. Disney was originally founded on October ...
artists John Hench and Art Riley, voice talent
Paul Frees
Solomon Hersh "Paul" Frees (June 22, 1920November 2, 1986) was an American actor, comedian, impressionist, and vaudevillian. He is known for his work on Metro-Goldwyn-Mayer, Walter Lantz, Rankin/Bass, and Walt Disney theatrical cartoons during ...
, and scientific expert
Heinz Haber
Heinz Haber (May 15, 1913 in Mannheim – February 13, 1990 in Hamburg) was a German physicist and science writer who primarily became known for his TV programs and books about physics and environmental subjects. His lucid style of explainin ...
, who had worked on the Disney space shows. It was released on a bill with ''
Darby O'Gill and the Little People
''Darby O'Gill and the Little People'' is a 1959 American fantasy adventure film produced by Walt Disney Productions, adapted from the ''Darby O'Gill'' stories of Herminie Templeton Kavanagh. Directed by Robert Stevenson and written by Lawrence E ...
''. In 1959, it was nominated for an
Academy Award
The Academy Awards, better known as the Oscars, are awards for artistic and technical merit for the American and international film industry. The awards are regarded by many as the most prestigious, significant awards in the entertainment ind ...
Ludwig Von Drake
Professor Ludwig Von Drake is a cartoon character created in 1961 by The Walt Disney Company. He is the paternal uncle of Donald Duck. He was first introduced as the presenter (and singer of " The Spectrum Song") in the cartoon ''An Adventure in ...
.
The film was made available to schools and became one of the most popular educational films ever made by Disney. As
Walt Disney
Walter Elias Disney (; December 5, 1901December 15, 1966) was an American animator, film producer and entrepreneur. A pioneer of the American animation industry, he introduced several developments in the production of cartoons. As a film p ...
himself explained, "The cartoon is a good medium to stimulate interest. We have recently explained mathematics in a film and in that way excited public interest in this very important subject."
The short was released on November 11, 2008 on '' Walt Disney Treasures: The Chronological Donald, Volume Four: 1951-1961''.
Additional releases include:
*1988 – ''Walt Disney Mini Classics: Donald in Mathmagic Land'' (VHS)
*2007 – ''Donald in Mathmagic Land'' (DVD exclusive to the Disney Movie Club)
*2009 – ''Donald in Mathmagic Land'' (DVD)
In other media
* A
comic book
A comic book, also called comicbook, comic magazine or (in the United Kingdom and Ireland) simply comic, is a publication that consists of comics art in the form of sequential juxtaposed panels that represent individual scenes. Panels are of ...
adaptation was made, scripted by
Don R. Christensen
Donald Ragnvald Christensen (July 6, 1916 – October 18, 2006) was an American animator, cartoonist, illustrator, writer and inventor. He was sometimes credited as "Don Arr".
Christensen was a graduate of the Minneapolis College of Art and Des ...
, pencilled by
Tony Strobl
Anthony Joseph Strobl ( ; May 12, 1915 – December 29, 1991) was an American comics artist and animator. He was born in Cleveland, Ohio and attended Cleveland School of Art from 1933–37, with Jerry Siegel and Joe Shuster, who actually g ...
, and inked by Steve Steere. However, this version differs in some ways from the original film version, providing a better context for Donald's excursion into Mathmagic Land.
* The '' House of Mouse'' episode "Gone Goofy" features an advertisement for Mathmagic Land at the end.