Bundling problem

Paata Ivanisvili

University of California, Irvine

2019

MARTHCOUNTS competition

Paata Ivanisvili University of California, Irvine Bundling problem

What is this?

Paata Ivanisvili University of California, Irvine Bundling problem

What is this?

Paata Ivanisvili University of California, Irvine Bundling problem

What is this?

Armadillo

Paata Ivanisvili University of California, Irvine Bundling problem

What is this?

Armadillo

Paata Ivanisvili University of California, Irvine Bundling problem

Armadillo

Paata Ivanisvili University of California, Irvine Bundling problem

Armadillo

Paata Ivanisvili University of California, Irvine Bundling problem

Lovely Armadillo

Paata Ivanisvili University of California, Irvine Bundling problem

Bronze Armadillo Sculpture by Adam Binder (UK)

Paata Ivanisvili University of California, Irvine Bundling problem

Sleeping armadillos

They usually sleep up to 16 hours each day.

Paata Ivanisvili University of California, Irvine Bundling problem

Sleeping armadillos

They usually sleep up to 16 hours each day.

Paata Ivanisvili University of California, Irvine Bundling problem

Sleeping armadillos

They usually sleep up to 16 hours each day.

Paata Ivanisvili University of California, Irvine Bundling problem

A question of Larry Glasser and Sydney Davison

Larry Glasser Sydney Davison

Question: Why do we see this?

Paata Ivanisvili University of California, Irvine Bundling problem

A question of Larry Glasser and Sydney Davison

Larry Glasser Sydney Davison

Question: Why do we see this?

Paata Ivanisvili University of California, Irvine Bundling problem

A question of Larry Glasser and Sydney Davison

Larry Glasser Sydney Davison

Question: Why do we see this?

Answer: Presumably animals keep each other warm by huddlingtogether, i.e., decreases the total rate of loss of heat.

Confirmed numerically by Glasser and Davison (1978).Mathematical proof was given by Alexander Eremenko (2003).

Paata Ivanisvili University of California, Irvine Bundling problem

A question of Larry Glasser and Sydney Davison

Larry Glasser Sydney Davison

Question: Why do we see this?Answer: Presumably animals keep each other warm by huddlingtogether,

i.e., decreases the total rate of loss of heat.

Confirmed numerically by Glasser and Davison (1978).Mathematical proof was given by Alexander Eremenko (2003).

Paata Ivanisvili University of California, Irvine Bundling problem

A question of Larry Glasser and Sydney Davison

Larry Glasser Sydney Davison

Question: Why do we see this?Answer: Presumably animals keep each other warm by huddlingtogether, i.e., decreases the total rate of loss of heat.

Confirmed numerically by Glasser and Davison (1978).Mathematical proof was given by Alexander Eremenko (2003).

Paata Ivanisvili University of California, Irvine Bundling problem

A question of Larry Glasser and Sydney Davison

Larry Glasser Sydney Davison

Question: Why do we see this?Answer: Presumably animals keep each other warm by huddlingtogether, i.e., decreases the total rate of loss of heat.

Confirmed numerically by Glasser and Davison (1978).

Mathematical proof was given by Alexander Eremenko (2003).

Paata Ivanisvili University of California, Irvine Bundling problem

A question of Larry Glasser and Sydney Davison

Larry Glasser Sydney Davison

Question: Why do we see this?Answer: Presumably animals keep each other warm by huddlingtogether, i.e., decreases the total rate of loss of heat.

Confirmed numerically by Glasser and Davison (1978).Mathematical proof was given by Alexander Eremenko (2003).

Paata Ivanisvili University of California, Irvine Bundling problem

A question of Larry Glasser and Sydney Davison

Larry Glasser Sydney Davison

Question: Why do we see this?Answer: Presumably animals keep each other warm by huddlingtogether, i.e., decreases the total rate of loss of heat.

Confirmed numerically by Glasser and Davison (1978).Mathematical proof was given by Alexander Eremenko (2003).

Paata Ivanisvili University of California, Irvine Bundling problem

A question of Alexander Eremenko

Alexander Eremenko (Distinguished professor at Purdue University)

Question: What about the individual rates of loss of heat?

Eremenko’s thoughts: each individual animal feels only his own rateof loss of heat. Therefore the behaviour of the animals could bedriven by individual feelings but not the abstract “common goal”.

Paata Ivanisvili University of California, Irvine Bundling problem

A question of Alexander Eremenko

Alexander Eremenko (Distinguished professor at Purdue University)

Question: What about the individual rates of loss of heat?

Eremenko’s thoughts: each individual animal feels only his own rateof loss of heat. Therefore the behaviour of the animals could bedriven by individual feelings but not the abstract “common goal”.

Paata Ivanisvili University of California, Irvine Bundling problem

armadillo A armadillo B

Given: Two spherical armadillos of different sizes (A > B).

Bothhave equal positive temperature. Temperature outside is zero.

Question: Should armadillo A be as close as possible to armadilloB to minimize his own rate of loss of heat?

Answer: No and Yes. Theorem [P. Ivanisvili, 2016].If A >2B then A should keep a certain nonzero distance to minimizehis rate of loss of heat, but B should minimize the distance to A.If B

armadillo A armadillo B

Given: Two spherical armadillos of different sizes (A > B). Bothhave equal positive temperature.

Temperature outside is zero.

Question: Should armadillo A be as close as possible to armadilloB to minimize his own rate of loss of heat?

Answer: No and Yes. Theorem [P. Ivanisvili, 2016].If A >2B then A should keep a certain nonzero distance to minimizehis rate of loss of heat, but B should minimize the distance to A.If B

armadillo A armadillo B

Given: Two spherical armadillos of different sizes (A > B). Bothhave equal positive temperature. Temperature outside is zero.

Question: Should armadillo A be as close as possible to armadilloB to minimize his own rate of loss of heat?

Answer: No and Yes. Theorem [P. Ivanisvili, 2016].If A >2B then A should keep a certain nonzero distance to minimizehis rate of loss of heat, but B should minimize the distance to A.If B

armadillo A armadillo B

Given: Two spherical armadillos of different sizes (A > B). Bothhave equal positive temperature. Temperature outside is zero.

Question: Should armadillo A be as close as possible to armadilloB to minimize his own rate of loss of heat?

Answer: No and Yes. Theorem [P. Ivanisvili, 2016].If A >2B then A should keep a certain nonzero distance to minimizehis rate of loss of heat, but B should minimize the distance to A.If B

armadillo A armadillo B

Given: Two spherical armadillos of different sizes (A > B). Bothhave equal positive temperature. Temperature outside is zero.

Question: Should armadillo A be as close as possible to armadilloB to minimize his own rate of loss of heat?

Answer: No and Yes.

Theorem [P. Ivanisvili, 2016].If A >2B then A should keep a certain nonzero distance to minimizehis rate of loss of heat, but B should minimize the distance to A.If B

armadillo A armadillo B

Given: Two spherical armadillos of different sizes (A > B). Bothhave equal positive temperature. Temperature outside is zero.

Question: Should armadillo A be as close as possible to armadilloB to minimize his own rate of loss of heat?

Answer: No and Yes. Theorem [P. Ivanisvili, 2016].

If A >2B then A should keep a certain nonzero distance to minimizehis rate of loss of heat, but B should minimize the distance to A.If B

armadillo A armadillo B

Given: Two spherical armadillos of different sizes (A > B). Bothhave equal positive temperature. Temperature outside is zero.

Question: Should armadillo A be as close as possible to armadilloB to minimize his own rate of loss of heat?

Answer: No and Yes. Theorem [P. Ivanisvili, 2016].If A >2B

then A should keep a certain nonzero distance to minimizehis rate of loss of heat, but B should minimize the distance to A.If B

armadillo A armadillo B

Given: Two spherical armadillos of different sizes (A > B). Bothhave equal positive temperature. Temperature outside is zero.

Question: Should armadillo A be as close as possible to armadilloB to minimize his own rate of loss of heat?

Answer: No and Yes. Theorem [P. Ivanisvili, 2016].If A >2B then A should keep a certain nonzero distance to minimizehis rate of loss of heat,

but B should minimize the distance to A.If B

armadillo A armadillo B

Given: Two spherical armadillos of different sizes (A > B). Bothhave equal positive temperature. Temperature outside is zero.

Question: Should armadillo A be as close as possible to armadilloB to minimize his own rate of loss of heat?

Answer: No and Yes. Theorem [P. Ivanisvili, 2016].If A >2B then A should keep a certain nonzero distance to minimizehis rate of loss of heat, but B should minimize the distance to A.

If B

armadillo A armadillo B

Given: Two spherical armadillos of different sizes (A > B). Bothhave equal positive temperature. Temperature outside is zero.

Question: Should armadillo A be as close as possible to armadilloB to minimize his own rate of loss of heat?

Answer: No and Yes. Theorem [P. Ivanisvili, 2016].If A >2B then A should keep a certain nonzero distance to minimizehis rate of loss of heat, but B should minimize the distance to A.If B

Thank you

Paata Ivanisvili University of California, Irvine Bundling problem