Category: Engagement

My Mathematical Magic Show: Part 10

This magic trick is an optical illusion instead of a pure magic trick, but it definitely is a crowd-pleaser. This illusion is called Sugihara’s Impossible Cylinder:

This is actually a mathematical magic trick. As detailed by David Richeson in Math Horizons, there is a fair amount of math that goes into creating this unique shape. He also provided this interacted Geogebra applet as well as a printable pdf file for creating this illusion.

Predicate Logic and Popular Culture (Part 275): Florida Georgia Line

Let P be the set of all people, and let f(x) be the amount that x loves you. Translate the logical statement

\forall x \in P(f(x) \le f(\hbox{God}) \land f(x) \le f(\hbox{your mama}) \land f(x) \le f(\hbox{I})).

This matches the chorus of the crossover hit “God, Your Mama, and Me” by Florida Georgia Line, featuring the Backstreet Boys.

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Context: This semester, I taught discrete mathematics for the first time. Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 274): George Jones

Let T be the set of all times, and let L(t) be the statement “He loves her at time t. Translate the logical statement

\forall t \in T(((t < 0) \Longrightarrow L(t)) \land ((t \ge 0) \Longrightarrow \sim L(t))),

where time 0 is today.

Of course, this matches the quintessential country song “He Stopped Loving Her Today” by George Jones.

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Context: This semester, I taught discrete mathematics for the first time. Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 273): Beauty and the Beast

Let P be the set of all people, let S(x) be the statement “x is slick as Gaston,” let Q(x) be the statement “x is quick as Gaston,” and let N(x) be the statement “x‘s neck is as thick as Gaston’s neck.” Translate the logical statement

\forall x \in P \sim(S(x) \lor Q(x) \lor N(x))

This is just one example that I pulled from the silly song “Gaston” from “Beauty and the Beast.”

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Context: This semester, I taught discrete mathematics for the first time. Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 272): Beauty and the Beast

Let T be the set of all things, let D(x) be the statement “x is a dinner,” let F(x) be the statement “x is in France,” and let S(x) be the statement “x is second-best.” Translate the logical statement

\forall x \in T (D(x) \land F(x) \Longrightarrow \sim S(x))

This matches a line from the incurably catchy “Be Our Guest” from “Beauty and the Beast.”

green line

Context: This semester, I taught discrete mathematics for the first time. Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 271): Pirates of the Caribbean

Let T be the set of all times, and let D(t) be the statement “At time t, you can trust a dishonest man to be dishonest.” Translate the logical statement

\forall t \in T (D(t))

This matches a line from the movie “Pirates of the Caribbean: The Curse of the Black Pearl.”

green line

Context: This semester, I taught discrete mathematics for the first time. Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 270): Naruto Shippuden

Let P be the set of all places, let L(x) be the statement “There is light at x,” and let S(x) be the statement “There are shadows to be found at x.” Translate the logical statement

\forall x \in P (L(x) \Longrightarrow S(x))

This matches one of the lines from the anime “Naruto Shippuden.”

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Context: This semester, I taught discrete mathematics for the first time. Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.

Predicate Logic and Popular Culture (Part 269): Hamilton

Let p be the statement “We lay a strong enough foundation,” let q be the statement “We’ll pass it on to you,” let r be the statement “We’ll give the world to you,” and let s be the statement “You’ll blow us all away.” Translate the logical statement

p \Longrightarrow q \land r \land s

This matches one of the lines from the lullaby “Dear Theodosia” from the hit musical “Hamilton.”

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Context: This semester, I taught discrete mathematics for the first time. Part of the discrete mathematics course includes an introduction to predicate and propositional logic for our math majors. As you can probably guess from their names, students tend to think these concepts are dry and uninteresting even though they’re very important for their development as math majors.

In an effort to making these topics more appealing, I spent a few days mining the depths of popular culture in a (likely futile) attempt to make these ideas more interesting to my students. In this series, I’d like to share what I found. Naturally, the sources that I found have varying levels of complexity, which is appropriate for students who are first learning prepositional and predicate logic.

When I actually presented these in class, I either presented the logical statement and had my class guess the statement in actual English, or I gave my students the famous quote and them translate it into predicate logic. However, for the purposes of this series, I’ll just present the statement in predicate logic first.